{"id":109430,"date":"2026-09-24T04:08:37","date_gmt":"2026-09-23T20:08:37","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/109430.html"},"modified":"2026-09-24T04:08:37","modified_gmt":"2026-09-23T20:08:37","slug":"%e6%b7%b7%e6%b2%8c%e6%8b%93%e6%89%91%e5%ad%a6%ef%bc%88hdt%ef%bc%89%e9%87%8f%e5%ad%90%e5%8a%9b%e5%ad%a6%e7%af%87","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/109430.html","title":{"rendered":"\u6df7\u6c8c\u62d3\u6251\u5b66\uff08HDT\uff09\u91cf\u5b50\u529b\u5b66\u7bc7"},"content":{"rendered":"<h3>\u6458\u8981<\/h3>\n<p>\u73b0\u4ee3\u79d1\u5b66\u5373\u5c06\u91cd\u6784\u3002<\/p>\n<p>\u6316\u51fa\u5404\u79cd\u672a\u7ecf\u9a8c\u8bc1\u7684\u5047\u8bbe&#xff0c;\u4f1a\u8ba9\u90a3\u4e9b\u4f2a\u903b\u8f91\u3001\u4f2a\u79d1\u5b66\u65e0\u6cd5\u9041\u5f62\u3002<\/p>\n<p>\u5fae\u89c2\u7269\u7406\u4e2d\u6709\u4e00\u7ec4\u73b0\u8c61&#xff0c;\u5176\u89c2\u6d4b\u8bfb\u6570\u5927\u591a\u4ee5\u6982\u7387\u5f62\u5f0f\u7ed9\u51fa&#xff1a;\u91cf\u5b50\u53e0\u52a0\u3001\u6d4b\u4e0d\u51c6\u539f\u7406\u3001\u81ea\u65cb\u3001\u91cf\u5b50\u5316\u3001\u6ce2\u7c92\u4e8c\u8c61\u6027\u3001\u91cf\u5b50\u96a7\u7a7f\u3001\u771f\u7a7a\u6da8\u843d\u3001\u91cf\u5b50\u7ea0\u7f20\u3002\u8fd9\u4e9b\u73b0\u8c61\u5728\u73b0\u6709\u7406\u8bba\u4e2d\u5404\u81ea\u6709\u4e00\u6761\u89e3\u91ca&#xff0c;\u5f7c\u6b64\u4e4b\u95f4\u5e76\u4e0d\u7edf\u4e00&#xff1b;\u516b\u6761\u89e3\u91ca\u6240\u4f9d\u8d56\u7684\u5047\u8bbe\u4e92\u4e0d\u76f8\u540c&#xff0c;\u4e5f\u6ca1\u6709\u4e00\u6761\u80fd\u7531\u66f4\u57fa\u672c\u7684\u524d\u63d0\u63a8\u51fa\u3002<\/p>\n<p>\u672c\u6587\u8003\u5bdf\u8fd9\u516b\u4e2a\u73b0\u8c61\u7684\u5171\u540c\u7279\u5f81&#xff0c;\u5e76\u63d0\u51fa&#xff1a;\u5b83\u4eec\u4e4b\u6240\u4ee5\u5927\u591a\u5448\u73b0\u6982\u7387\u5f62\u5f0f&#xff0c;\u539f\u56e0\u5728\u4e8e\u89c2\u6d4b\u5173\u7cfb\u672c\u8eab&#xff0c;\u800c\u975e\u88ab\u89c2\u6d4b\u5bf9\u8c61\u672c\u8eab\u3002<\/p>\n<p>\u672c\u6587\u5f15\u5165\u4e00\u4e2a\u91cf\u2014\u2014\u91c7\u6837\u6bd4 N\u2014\u2014\u7528\u4ee5\u523b\u753b\u89c2\u6d4b\u7a97\u53e3\u4e0e\u5bf9\u8c61\u5185\u7980\u53d8\u5316\u5468\u671f\u4e4b\u6bd4&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">N&#061;R\u2009\u0394t\u91c7\u6837\u03c4objN &#061; \\\\frac{\\\\mathcal{R}\\\\,\\\\Delta t_{\u91c7\u6837}}{\\\\tau_{obj}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.3324em;vertical-align: -0.9721em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1132em\">\u03c4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1132em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">bj<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord cjk_fallback mtight\">\u91c7\u6837<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9721em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5f53 N \u2264 1\/2 \u65f6&#xff0c;\u91c7\u6837\u6240\u5f97\u53ef\u4ee5\u8fd8\u539f\u5bf9\u8c61\u7684\u53d8\u5316\u8fc7\u7a0b&#xff1b;\u5f53 N &gt; 1\/2 \u65f6&#xff0c;\u91c7\u6837\u6240\u5f97\u4e0d\u518d\u662f\u8fc7\u7a0b\u672c\u8eab&#xff0c;\u800c\u662f\u5bf9\u8c61\u5728\u591a\u4e2a\u76f8\u4f4d\u4e0a\u7684\u53e0\u52a0&#xff0c;\u5176\u8bfb\u6570\u8868\u73b0\u4e3a\u53d6\u503c\u8303\u56f4\u4e0e\u76f8\u5e94\u7684\u5206\u5e03\u3002\u8fd9\u4e00\u7ed3\u8bba\u6765\u81ea\u91c7\u6837\u5b9a\u7406&#xff0c;\u5c5e\u6570\u5b66&#xff0c;\u4e0d\u4f9d\u8d56\u7279\u5b9a\u7684\u7269\u7406\u6846\u67b6\u3002<\/p>\n<p>\u636e\u6b64&#xff0c;\u672c\u6587\u7ed9\u51fa&#xff1a;\u5fae\u89c2\u73b0\u8c61\u4e2d\u7684\u6982\u7387\u5f62\u5f0f&#xff0c;\u4f4d\u4e8e\u89c2\u6d4b\u5173\u7cfb\u4e00\u4fa7\u3002\u6539\u53d8\u89c2\u6d4b\u7a97\u53e3 \u0394t \u91c7\u6837&#xff0c;\u8bfb\u6570\u7684\u5206\u5e03\u5f62\u5f0f\u968f\u4e4b\u6539\u53d8&#xff0c;\u800c\u5bf9\u8c61\u672c\u8eab\u5e76\u672a\u6539\u53d8\u3002<\/p>\n<p>\u672c\u6587\u7684\u8d77\u70b9\u6709\u4e09\u6761&#xff0c;\u5217\u4e8e\u7b2c 1 \u8282&#xff1a;\u6df7\u6c8c\u672c\u4f53\u3001\u8fc7\u7a0b\u5b9e\u5728\u3001\u89c2\u6d4b\u5373\u6709\u9650\u91c7\u6837\u3002\u4e09\u6761\u4e0d\u7531\u89c2\u6d4b\u63a8\u51fa&#xff0c;\u4e5f\u4e0d\u9700\u8981\u7531\u89c2\u6d4b\u63a8\u51fa\u2014\u2014\u8d77\u70b9\u662f\u88ab\u9009\u7684&#xff0c;\u4e0d\u662f\u88ab\u8bc1\u7684\u3002\u4f5c\u4e3a\u5bf9\u7167&#xff0c;\u65e2\u6709\u8def\u5f84\u7684\u8d77\u70b9\u540c\u6837\u662f\u4e00\u6761\u65ad\u8a00&#xff1a;\u5fae\u89c2\u5bf9\u8c61\u672c\u8eab\u4e0d\u5177\u5907\u786e\u5b9a\u7684\u53d8\u5316\u8fc7\u7a0b\u3002\u4e24\u6761\u8d77\u70b9\u5728\u6b64\u5904\u5747\u65e0\u53ef\u5224\u4e4b\u636e&#xff0c;\u5176\u5206\u91ce\u7531\u5404\u81ea\u9700\u8981\u591a\u5c11\u9644\u52a0\u5047\u8bbe\u3001\u5404\u81ea\u80fd\u957f\u51fa\u591a\u5c11\u4e1c\u897f\u6765\u5224\u5b9a\u3002<\/p>\n<p>\u5728\u7b2c 3 \u8282\u4e2d&#xff0c;\u672c\u6587\u5bf9\u516b\u4e2a\u73b0\u8c61\u9010\u4e00\u7ed9\u51fa\u4e24\u79cd\u8868\u8ff0&#xff0c;\u5e76\u5217\u6446\u51fa&#xff0c;\u4e0d\u4f5c\u5426\u5b9a\u3002\u5728\u7b2c 4 \u8282\u4e2d\u7ed9\u51fa\u4e09\u6761\u53ef\u7531\u89c2\u6d4b\u68c0\u9a8c\u7684\u540e\u679c\u3002\u7b2c 5 \u8282\u5217\u51fa\u4e94\u9879\u5c1a\u672a\u8d70\u5b8c\u7684\u8def\u3002<\/p>\n<p>\u5168\u6587\u771f\u6b63\u7684\u5730\u57fa\u53ea\u6709\u4e00\u53e5&#xff1a;<\/p>\n<p>\u7528\u6700\u7b80\u5355\u7684\u4e1c\u897f\u89e3\u91ca\u6700\u591a\u7684\u73b0\u8c61\u2014\u2014\u7528\u80fd\u91cf\u7684\u8fd0\u52a8\u4e0e\u6d41\u53d8&#xff0c;\u89e3\u91ca\u63a5\u8fd1\u5168\u90e8\u7684\u7269\u7406\u73b0\u8c61\u3002\u8fd9\u4e2a\u7406\u8bba\u8fdf\u65e9\u4f1a\u6210\u4e3a\u7269\u7406\u5b66\u7684\u5730\u57fa\u3002<\/p>\n<p>\u8fd9\u662f\u4e00\u573a\u6218\u4e89\u3002 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&#061; \u8d28\u91cf \u00f7 \u4f53\u79ef\u3002\u5206\u5b50\u662f\u5e73\u5747\u503c&#xff08;\u539f\u7406\u4e94&#xff09;&#xff0c;\u5206\u6bcd\u662f\u4eba\u4e3a\u754c\u5b9a\u7684\u8303\u56f4&#xff08;\u7c92\u5b50\u6ca1\u6709\u8fb9\u754c&#xff0c;\u5411\u5916\u8fde\u7eed\u7a00\u8584&#xff0c;\u4e0e\u771f\u7a7a\u65e0\u522b\u2014\u2014\u89c1\u539f\u7406\u4e00&#xff09;\u3002\u4e24\u4e2a\u91cf\u90fd\u662f\u7b97\u51fa\u6765\u7684&#xff0c;\u6bd4\u503c\u81ea\u7136\u4e5f\u662f\u7b97\u51fa\u6765\u7684\u3002<\/p>\n<p>\u800c\u771f\u5b9e\u7684\u5206\u5e03\u5e76\u4e0d\u5747\u5300\u3002\u7531\u300a\u80fd\u91cf\u4e00\u5143\u76f8\u53d8\u8bba\u300b\u00a71&#xff08;\u6728\u661f\u6a21\u578b&#xff0f;\u53f0\u98ce\u5185\u6838&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\u5bc6\u5ea6\u5cf0\u503c\u4e0d\u5728\u4e2d\u5fc3&#xff0c;\u800c\u5728\u7d27\u8d34\u4e2d\u5fc3\u7684\u4e00\u5708\u73af\u5e26\u4e0a\u2014\u2014\u76f8\u5f53\u4e8e\u53f0\u98ce\u7684\u773c\u58c1&#xff1b;<\/li>\n<li>\u4e2d\u5fc3\u662f\u4f4e\u5bc6\u5ea6\u7684\u8f6c\u8fd0\u4e2d\u67a2&#xff0c;\u6709\u573a\u3001\u6709\u541e\u5410&#xff0c;\u5e76\u975e\u7a7a\u65e0&#xff1b;<\/li>\n<li>\u518d\u5411\u5916\u8fde\u7eed\u7a00\u8584&#xff0c;\u76f4\u81f3\u4e0e\u5b87\u5b99\u771f\u7a7a\u96be\u4ee5\u5206\u8fa8\u3002<\/li>\n<\/ul>\n<p>\u6240\u4ee5&#034;\u5e73\u5747\u5bc6\u5ea6&#034;\u662f\u4e00\u4e2a\u8bb0\u8d26\u5de5\u5177&#xff0c;\u4e0d\u662f\u7c92\u5b50\u7684\u771f\u5b9e\u5206\u5e03\u3002 \u628a\u5e73\u5747\u503c\u5f53\u6210\u7c92\u5b50\u7684\u5c5e\u6027&#xff0c;\u4e0e\u628a\u73b0\u8c61\u5f53\u6210\u5b9e\u4f53&#xff0c;\u662f\u540c\u4e00\u7c7b\u505a\u6cd5\u3002<\/p>\n<p>\u8fd9\u4e00\u6761\u5bf9\u672c\u6587\u7684\u610f\u4e49&#xff1a;\u65e2\u7136\u5bf9\u8c61\u81ea\u8eab\u5728\u6d41\u53d8\u3001\u5728\u4ea4\u6362\u3001\u4e14\u5176\u5206\u5e03\u672c\u4e0d\u5747\u5300&#xff0c;\u90a3\u4e48&#034;\u5bf9\u8c61\u5177\u6709\u786e\u5b9a\u4e0d\u53d8\u7684\u5c5e\u6027&#034;\u8fd9\u4e00\u9884\u8bbe\u4ece\u8d77\u70b9\u4e0a\u5c31\u4e0d\u6210\u7acb\u3002\u8bfb\u6570\u5448\u73b0\u4e3a\u5206\u5e03&#xff0c;\u4e0d\u53ea\u56e0\u4e3a\u91c7\u6837\u7a97\u53e3\u592a\u957f&#xff0c;\u4e5f\u56e0\u4e3a\u5bf9\u8c61\u672c\u8eab\u5c31\u5728\u53d8\u3002 \u8fd9\u4e24\u6761\u5408\u8d77\u6765&#xff0c;\u624d\u662f\u672c\u6587\u5bf9\u6982\u7387\u5f62\u5f0f\u7684\u5b8c\u6574\u8bf4\u660e\u2014\u2014\u524d\u8005\u6765\u81ea\u89c2\u6d4b\u4e00\u4fa7&#xff08;\u539f\u7406\u4e03&#xff09;&#xff0c;\u540e\u8005\u6765\u81ea\u5bf9\u8c61\u4e00\u4fa7&#xff08;\u539f\u7406\u4e94&#xff09;\u3002<\/p>\n<hr \/>\n<h3>2 \u91c7\u6837\u6bd4<\/h3>\n<h4>2.1 \u89c2\u6d4b\u7684\u7ed3\u6784<\/h4>\n<p>\u7531\u539f\u7406\u4e09&#xff0c;\u89c2\u6d4b\u4e0d\u662f\u4e00\u4e2a\u77ac\u65f6\u52a8\u4f5c&#xff0c;\u800c\u662f\u4e00\u6bb5\u6709\u957f\u5ea6\u7684\u7a97\u53e3\u3002\u5728\u8fd9\u6bb5\u7a97\u53e3\u5185&#xff0c;\u5bf9\u8c61\u6301\u7eed\u53d8\u5316&#xff1b;\u89c2\u6d4b\u6240\u5f97\u662f\u8fd9\u6bb5\u65f6\u95f4\u5185\u53d8\u5316\u7684\u7d2f\u79ef\u3002<\/p>\n<p>\u8bbe\u5bf9\u8c61\u81ea\u8eab\u53d8\u5316\u4e00\u5468\u6240\u9700\u7684\u65f6\u95f4\u4e3a \u03c4_obj&#xff0c;\u89c2\u6d4b\u7a97\u53e3\u957f\u5ea6\u4e3a \u0394t \u91c7\u6837\u3002\u4e8c\u8005\u4e4b\u6bd4\u51b3\u5b9a\u4e86\u89c2\u6d4b\u6240\u5f97\u7684\u6027\u8d28\u3002<\/p>\n<h4>\u5b9a\u4e49 2.1&#xff08;\u91c7\u6837\u6bd4&#xff09;<\/h4>\n<p>\u8bbe\u7ed3\u6784\u76f8\u5bf9\u6027\u7cfb\u6570 R \u968f\u89c2\u5bdf\u8005\u4e0e\u5bf9\u8c61\u7684\u5c3a\u5ea6\u6bd4\u53d8\u5316&#xff08;\u89c1\u300aHDT \u5bf9\u65f6\u95f4\u7684\u91cd\u65b0\u89e3\u8bfb\u300b\u00a76&#xff09;&#xff0c;\u91c7\u6837\u6bd4\u5b9a\u4e49\u4e3a<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">N&#061;R\u2009\u0394t\u91c7\u6837\u03c4objN &#061; \\\\frac{\\\\mathcal{R}\\\\,\\\\Delta t_{\u91c7\u6837}}{\\\\tau_{obj}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.3324em;vertical-align: -0.9721em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1132em\">\u03c4<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1132em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">bj<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathcal\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord cjk_fallback mtight\">\u91c7\u6837<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9721em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>N \u7684\u542b\u4e49\u662f&#xff1a;\u5728\u89c2\u6d4b\u8005\u91c7\u4e00\u6b21\u6837\u7684\u8fd9\u6bb5\u65f6\u95f4\u91cc&#xff0c;\u5bf9\u8c61\u53d8\u5316\u4e86\u591a\u5c11\u4e2a\u5468\u671f\u3002N \u8d8a\u5c0f&#xff0c;\u91c7\u6837\u8d8a\u5bc6&#xff1b;N \u8d8a\u5927&#xff0c;\u91c7\u6837\u8d8a\u7c97\u3002<\/p>\n<h4>\u539f\u7406\u516d&#xff08;\u91c7\u6837\u8fd8\u539f\u539f\u7406&#xff09;<\/h4>\n<p>\u5f53 N \u2264 1\/2 \u65f6&#xff0c;\u7531\u91c7\u6837\u6240\u5f97\u5e8f\u5217\u53ef\u4ee5\u8fd8\u539f\u5bf9\u8c61\u7684\u53d8\u5316\u8fc7\u7a0b\u3002<\/p>\n<p>\u4f9d\u636e&#xff1a;\u91c7\u6837\u5b9a\u7406&#xff08;Nyquist\u2013Shannon&#xff09;\u3002\u91c7\u6837\u9891\u7387\u4e0d\u4f4e\u4e8e\u88ab\u91c7\u4fe1\u53f7\u9891\u7387\u7684\u4e24\u500d\u65f6&#xff0c;\u539f\u4fe1\u53f7\u53ef\u7531\u91c7\u6837\u5e8f\u5217\u552f\u4e00\u91cd\u5efa\u3002<\/p>\n<p>\u8bf4\u660e&#xff1a;\u6b64\u65f6\u89c2\u6d4b\u8005\u91c7\u5f97\u6bd4\u5bf9\u8c61\u53d8\u5f97\u5feb&#xff0c;\u53d8\u5316\u8fc7\u7a0b\u53ef\u4ee5\u4e00\u5e27\u4e00\u5e27\u770b\u4e0b\u6765&#xff0c;\u8bfb\u6570\u8868\u73b0\u4e3a\u786e\u5b9a\u503c\u3002<\/p>\n<h4>\u539f\u7406\u4e03&#xff08;\u6df7\u53e0\u539f\u7406&#xff09;<\/h4>\n<p>\u5f53 N &gt; 1\/2 \u65f6&#xff0c;\u91c7\u6837\u6240\u5f97\u4e0d\u518d\u662f\u5bf9\u8c61\u7684\u53d8\u5316\u8fc7\u7a0b&#xff0c;\u800c\u662f\u5bf9\u8c61\u5728\u591a\u4e2a\u76f8\u4f4d\u4e0a\u7684\u53e0\u52a0\u3002\u6b64\u65f6\u8bfb\u6570\u4e0d\u5448\u73b0\u4e3a\u786e\u5b9a\u503c&#xff0c;\u800c\u5448\u73b0\u4e3a\u53d6\u503c\u8303\u56f4\u53ca\u76f8\u5e94\u5206\u5e03\u3002<\/p>\n<p>\u4f9d\u636e&#xff1a;\u540c\u4e0a\u3002\u6761\u4ef6\u4e0d\u6ee1\u8db3\u65f6\u53d1\u751f\u6df7\u53e0&#xff0c;\u4e0d\u540c\u9891\u7387\u6210\u5206\u5728\u91c7\u6837\u540e\u4e0d\u53ef\u533a\u5206\u3002<\/p>\n<p>\u8bf4\u660e&#xff1a;\u6b64\u65f6\u5bf9\u8c61\u5728\u89c2\u6d4b\u8005\u91c7\u4e00\u6b21\u6837\u7684\u65f6\u95f4\u91cc\u5df2\u7ecf\u53d8\u5316\u4e86\u591a\u4e2a\u5468\u671f\u3002\u8fd9\u4e00\u683c\u91c7\u5230\u7684\u662f\u591a\u4e2a\u76f8\u4f4d\u53e0\u5728\u4e00\u8d77\u7684\u7ed3\u679c\u2014\u2014\u76f8\u4f4d\u4fe1\u606f\u88ab\u62b9\u5e73\u4e86&#xff0c;\u5269\u4e0b\u7684\u53ea\u80fd\u662f\u4e00\u4e2a\u53d6\u503c\u8303\u56f4\u548c\u76f8\u5e94\u7684\u5206\u5e03\u3002<\/p>\n<h4>2.2 \u4e00\u4e2a\u76f4\u63a5\u540e\u679c<\/h4>\n<p>\u7531\u539f\u7406\u4e03&#xff0c;\u8bfb\u6570\u7684\u5206\u5e03\u5f62\u5f0f\u53d6\u51b3\u4e8e \u0394t \u91c7\u6837 \u4e0e \u03c4_obj \u4e4b\u6bd4&#xff0c;\u800c\u4e0d\u662f\u53d6\u51b3\u4e8e\u5bf9\u8c61\u662f\u5426\u5177\u6709\u786e\u5b9a\u8fc7\u7a0b\u3002\u7531\u6b64&#xff1a;<\/p>\n<p>\u539f\u7406\u516b&#xff08;\u7a97\u53e3\u6539\u53d8&#xff0c;\u5206\u5e03\u968f\u4e4b\u6539\u53d8&#xff09;&#xff1a;\u5bf9\u540c\u4e00\u5bf9\u8c61&#xff0c;\u6539\u53d8 \u0394t \u91c7\u6837 \u53ef\u4ee5\u6539\u53d8\u8bfb\u6570\u7684\u5206\u5e03\u5f62\u5f0f\u3002\u5206\u5e03\u5f62\u5f0f\u7684\u6539\u53d8\u4e0d\u8574\u542b\u5bf9\u8c61\u672c\u8eab\u7684\u6539\u53d8\u3002<\/p>\n<p>\u539f\u7406\u4e5d&#xff08;\u7a97\u53e3\u56fa\u5b9a\u65f6\u4e24\u6761\u8d77\u70b9\u8bfb\u6570\u76f8\u540c&#xff09;&#xff1a;\u73b0\u6709\u5fae\u89c2\u89c2\u6d4b\u5747\u5b9e\u65bd\u4e8e N \u8fdc\u5927\u4e8e 1\/2 \u4e14\u7a97\u53e3\u56fa\u5b9a\u7684\u6761\u4ef6&#xff0c;\u6545\u5176\u8bfb\u6570\u591a\u8868\u73b0\u4e3a\u5206\u5e03\u5f62\u5f0f\u3002\u5728\u6b64\u6761\u4ef6\u4e0b&#xff0c;\u4e24\u6761\u8d77\u70b9\u7ed9\u51fa\u7684\u6570\u503c\u76f8\u540c&#xff1b;\u5206\u6b67\u51fa\u73b0\u5728\u89c2\u6d4b\u7a97\u53e3\u88ab\u6539\u53d8\u65f6&#xff08;\u89c1 \u00a74&#xff09;\u3002<\/p>\n<h4>2.3 \u91c7\u6837\u5b9a\u7406\u7684\u4f7f\u7528\u8303\u56f4<\/h4>\n<p>\u91c7\u6837\u5b9a\u7406\u5728\u672c\u6587\u4e2d\u4f5c\u4e3a\u6570\u5b66\u5de5\u5177\u4f7f\u7528\u3002\u8be5\u5b9a\u7406\u5c5e\u4e8e\u6570\u5b66&#xff0c;\u672c\u6587\u4f7f\u7528\u5176\u7ed3\u8bba&#xff0c;\u4e0d\u5f15\u5165\u4e0e\u4e4b\u4f34\u968f\u7684\u7269\u7406\u5047\u8bbe\u3002\u672c\u6587\u4e5f\u6ca1\u6709\u4ece\u8be5\u5b9a\u7406\u63a8\u51fa\u539f\u7406\u4e8c\u2014\u2014\u539f\u7406\u4e8c\u662f\u8d77\u70b9&#xff0c;\u4e0d\u7531\u6570\u5b66\u5de5\u5177\u63a8\u51fa\u3002\u4e8c\u8005\u7684\u5206\u5de5\u662f&#xff1a;\u539f\u7406\u4e8c\u9648\u8ff0\u5bf9\u8c61\u4e00\u4fa7&#xff0c;\u539f\u7406\u4e03 \u9648\u8ff0\u8bfb\u6570\u4e00\u4fa7\u3002<\/p>\n<hr \/>\n<h3>3 \u516b\u4e2a\u73b0\u8c61<\/h3>\n<p>\u4ee5\u4e0b\u5404\u6761\u7ed3\u6784\u76f8\u540c&#xff1a;\u5148\u5982\u5b9e\u5199\u51fa\u8be5\u73b0\u8c61\u5728\u65e2\u6709\u7406\u8bba\u4e2d\u662f\u4ec0\u4e48\u2014\u2014\u5b9a\u4e49\u3001\u516c\u5f0f\u3001\u5b9e\u9a8c\u4e8b\u5b9e&#xff1b;\u968f\u540e\u7ed9\u51fa\u672c\u6587\u7684\u89e3\u8bfb\u3002\u65e2\u6709\u8868\u8ff0\u7167\u5b9e\u5199\u51fa&#xff0c;\u4e0d\u4f5c\u5426\u5b9a&#xff0c;\u53ea\u4f5c\u5bf9\u7167\u3002<\/p>\n<p>\u4e4b\u6240\u4ee5\u8981\u5148\u5199\u6e05\u695a\u5b83\u662f\u4ec0\u4e48&#xff1a;\u4e0d\u5199\u51fa\u5bf9\u65b9\u7684\u4e1c\u897f&#xff0c;\u8bfb\u8005\u65e0\u4ece\u5bf9\u7167&#xff0c;\u4e5f\u65e0\u4ece\u5224\u65ad\u672c\u6587\u7684\u89e3\u8bfb\u843d\u5728\u54ea\u4e00\u6bb5\u4e0a\u3002<\/p>\n<hr \/>\n<h4>3.1 \u91cf\u5b50\u53e0\u52a0<\/h4>\n<p>\u5b83\u662f\u4ec0\u4e48<\/p>\n<p>\u91cf\u5b50\u529b\u5b66\u628a\u7cfb\u7edf\u7684\u72b6\u6001\u5199\u6210\u6001\u77e2\u91cf |\u03c8\u27e9\u3002\u82e5 |\u03c8\u2081\u27e9 \u4e0e |\u03c8\u2082\u27e9 \u90fd\u662f\u8be5\u7cfb\u7edf\u53ef\u80fd\u53d6\u7684\u72b6\u6001&#xff0c;\u5219\u5b83\u4eec\u7684\u7ebf\u6027\u7ec4\u5408<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u2223\u03c8\u27e9&#061;a\u2223\u03c81\u27e9&#043;b\u2223\u03c82\u27e9|\\\\psi\\\\rangle &#061; a|\\\\psi_1\\\\rangle &#043; b|\\\\psi_2\\\\rangle<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c8<\/span><span class=\"mclose\">\u27e9<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">\u27e9<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">\u27e9<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u540c\u6837\u662f\u8be5\u7cfb\u7edf\u7684\u4e00\u4e2a\u53ef\u80fd\u72b6\u6001\u3002\u8fd9\u5c31\u662f\u53e0\u52a0\u539f\u7406&#xff0c;\u662f\u91cf\u5b50\u529b\u5b66\u7684\u57fa\u672c\u5047\u8bbe\u4e4b\u4e00\u3002\u6d4b\u91cf\u65f6&#xff0c;\u8bfb\u6570\u53ea\u7ed9\u51fa\u5176\u4e2d\u4e00\u4e2a\u7ed3\u679c&#xff0c;\u7ed9\u51fa |\u03c8\u2081\u27e9 \u7684\u6982\u7387\u4e3a |a|\u00b2&#xff0c;\u7ed9\u51fa |\u03c8\u2082\u27e9 \u7684\u6982\u7387\u4e3a |b|\u00b2&#xff0c;\u4e14 |a|\u00b2&#043;|b|\u00b2&#061;1\u3002<\/p>\n<p>\u53cc\u7f1d\u5b9e\u9a8c\u662f\u5176\u6807\u5fd7\u6027\u4f8b\u8bc1&#xff1a;\u7535\u5b50\u9010\u4e2a\u53d1\u5c04&#xff0c;\u6bcf\u6b21\u53ea\u5728\u5c4f\u4e0a\u7559\u4e0b\u4e00\u4e2a\u70b9&#xff1b;\u5927\u91cf\u70b9\u7d2f\u79ef\u540e\u5f62\u6210\u5e72\u6d89\u56fe\u6837\u3002\u5e38\u89c1\u7684\u8868\u8ff0\u662f&#034;\u7c92\u5b50\u540c\u65f6\u901a\u8fc7\u4e86\u4e24\u6761\u7f1d&#xff0c;\u4e0e\u81ea\u5df1\u5e72\u6d89&#034;\u3002\u859b\u5b9a\u8c14\u732b\u662f\u540c\u4e00\u539f\u7406\u7684\u601d\u60f3\u5b9e\u9a8c\u7248\u672c\u2014\u2014\u732b\u5904\u4e8e&#034;\u6b7b&#034;\u4e0e&#034;\u6d3b&#034;\u4e24\u4e2a\u72b6\u6001\u7684\u53e0\u52a0&#xff0c;\u76f4\u5230\u88ab\u89c2\u6d4b\u3002<\/p>\n<p>\u672c\u6587\u89e3\u8bfb<\/p>\n<p>\u732b\u4e0d\u662f\u53c8\u6b7b\u53c8\u6d3b&#xff0c;\u662f\u4f60\u4e0d\u77e5\u9053\u5b83\u662f\u6b7b\u8fd8\u662f\u6d3b\u3002<\/p>\n<p>\u91cf\u5b50\u53e0\u52a0\u6001\u4e0d\u662f\u5bf9\u8c61\u540c\u65f6\u5904\u4e8e\u591a\u4e2a\u72b6\u6001&#xff0c;\u662f\u89c2\u6d4b\u7684\u901f\u5ea6\u8ddf\u4e0d\u4e0a\u5b83\u7684\u53d8\u5316\u3002<\/p>\n<p>\u5bf9\u8c61\u5728\u82e5\u5e72\u6784\u578b\u4e4b\u95f4\u4ee5\u5468\u671f \u03c4_obj \u5feb\u901f\u5207\u6362\u3002\u89c2\u6d4b\u8005\u91c7\u4e00\u6b21\u6837\u9700\u8981 \u0394t \u91c7\u6837&#xff1b;\u5f53 N &gt; 1\/2 \u65f6&#xff08;\u539f\u7406\u4e03&#xff09;&#xff0c;\u5728\u91c7\u8fd9\u4e00\u6b21\u7684\u8fd9\u6bb5\u65f6\u95f4\u91cc&#xff0c;\u5bf9\u8c61\u5df2\u7ecf\u53d8\u5316\u4e86\u591a\u4e2a\u5468\u671f\u3002\u8fd9\u4e00\u683c\u91c7\u5230\u7684&#xff0c;\u662f\u8fd9\u591a\u4e2a\u76f8\u4f4d\u53e0\u5728\u4e00\u8d77\u7684\u7ed3\u679c\u2014\u2014\u76f8\u4f4d\u4fe1\u606f\u88ab\u62b9\u5e73\u4e86&#xff0c;\u5269\u4e0b\u7684\u53ea\u80fd\u662f\u4e00\u4e2a\u53d6\u503c\u8303\u56f4\u4e0e\u76f8\u5e94\u7684\u5206\u5e03\u3002<\/p>\n<p>\u4e8e\u662f |a|\u00b2\u3001|b|\u00b2 \u4e0d\u662f&#034;\u5bf9\u8c61\u540c\u65f6\u662f \u03c8\u2081 \u4e0e \u03c8\u2082&#034;\u7684\u5ea6\u91cf&#xff0c;\u800c\u662f\u89c2\u6d4b\u8005\u6765\u4e0d\u53ca\u5206\u8fa8\u65f6&#xff0c;\u5404\u6784\u578b\u5728\u91c7\u6837\u7a97\u53e3\u5185\u6240\u5360\u7684\u4efd\u989d\u3002<\/p>\n<p>\u89c2\u6d4b&#xff08;\u6d4b\u91cf&#xff09;\u4e4b\u540e\u8bfb\u6570\u53d8\u4e3a\u5355\u4e00\u503c&#xff0c;\u6b64\u4e8b\u7684\u542b\u4e49\u968f\u4e4b\u6539\u53d8&#xff1a;\u4e0d\u662f\u53e0\u52a0\u6001\u88ab\u7834\u574f\u4e86&#xff0c;\u662f\u8fd9\u4e00\u6b21\u91c7\u6837\u7ec8\u4e8e\u628a\u7a97\u53e3\u538b\u5f97\u591f\u7a84&#xff0c;\u53ea\u591f\u5bb9\u7eb3\u4e00\u4e2a\u6784\u578b\u3002 \u584c\u7f29\u4e0d\u662f\u5bf9\u8c61\u53d1\u751f\u4e86\u4ec0\u4e48&#xff0c;\u662f\u89c2\u6d4b\u5173\u7cfb\u53d8\u4e86\u3002<\/p>\n<p>\u4f9d\u636e&#xff1a;\u539f\u7406\u4e09\u3001\u539f\u7406\u4e03\u3002<\/p>\n<p>\u5bf9\u7167<\/p>\n<p>\u4e24\u79cd\u8868\u8ff0\u5728\u7a97\u53e3\u56fa\u5b9a\u7684\u6761\u4ef6\u4e0b\u7ed9\u51fa\u7684\u6570\u503c\u76f8\u540c\u3002\u5dee\u522b\u53ea\u6709\u4e00\u5904&#xff1a;<\/p>\n<ul>\n<li>\u65e2\u6709\u8868\u8ff0\u628a\u591a\u503c\u6027\u5f52\u4e8e\u5bf9\u8c61\u2014\u2014\u9700\u8981\u5047\u8bbe\u5bf9\u8c61\u53ef\u4ee5\u540c\u65f6\u5904\u4e8e\u591a\u4e2a\u72b6\u6001&#xff0c;\u5e76\u9700\u8981\u4e00\u4e2a\u989d\u5916\u673a\u5236&#xff08;\u584c\u7f29&#xff09;\u6765\u8bf4\u660e\u4e3a\u4ec0\u4e48\u6d4b\u91cf\u540e\u53ea\u5269\u4e00\u4e2a\u3002<\/li>\n<li>\u672c\u6587\u628a\u591a\u503c\u6027\u5f52\u4e8e\u91c7\u6837\u7a97\u53e3\u2014\u2014\u53ea\u9700\u5047\u8bbe\u91c7\u6837\u7a97\u53e3\u592a\u957f&#xff0c;\u4e0d\u9700\u8981\u989d\u5916\u673a\u5236&#xff1b;\u7a97\u53e3\u53d8\u7a84&#xff0c;\u8bfb\u6570\u81ea\u7136\u53d8\u786e\u5b9a\u3002<\/li>\n<\/ul>\n<p>\u524d\u8005\u8981\u589e\u52a0\u4e00\u6761\u5047\u8bbe\u548c\u4e00\u4e2a\u673a\u5236&#xff0c;\u540e\u8005\u4ec0\u4e48\u90fd\u4e0d\u7528\u52a0\u3002<\/p>\n<hr \/>\n<h4>3.2 \u6d4b\u4e0d\u51c6\u539f\u7406<\/h4>\n<p>\u5b83\u662f\u4ec0\u4e48<\/p>\n<p>1927 \u5e74\u7531\u6d77\u68ee\u5821\u7ed9\u51fa\u3002\u5bf9\u540c\u4e00\u5bf9\u8c61&#xff0c;\u5176\u4f4d\u7f6e\u8bfb\u6570\u4e0e\u52a8\u91cf\u8bfb\u6570\u7684\u4e0d\u786e\u5b9a\u5ea6\u4e4b\u79ef\u5b58\u5728\u4e0b\u754c&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u0394x\u22c5\u0394p\u2265\u210f2\\\\Delta x \\\\cdot \\\\Delta p \\\\geq \\\\frac{\\\\hbar}{2}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0519em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3659em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u210f<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8be5\u5173\u7cfb\u7531\u4f4d\u7f6e\u7b97\u7b26\u4e0e\u52a8\u91cf\u7b97\u7b26\u7684\u4e0d\u5bf9\u6613\u6027 [x\u0302, p\u0302] &#061; i\u210f \u63a8\u51fa\u3002\u76f8\u5e94\u8fd8\u6709\u80fd\u91cf\u4e0e\u65f6\u95f4\u7684\u4e00\u5bf9&#xff1a;\u0394E\u00b7\u0394t \u2265 \u210f\/2\u3002<\/p>\n<p>\u9700\u8981\u5199\u660e\u7684\u662f&#xff1a;\u8fd9\u4e00\u6761\u5728\u65e2\u6709\u7406\u8bba\u4e2d\u88ab\u8868\u8ff0\u4e3a\u5185\u7980\u9650\u5236&#xff0c;\u800c\u975e\u4eea\u5668\u7cbe\u5ea6\u4e0d\u8db3\u3002\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u5373\u4fbf\u4f7f\u7528\u7406\u60f3\u4eea\u5668&#xff0c;\u8be5\u4e0b\u754c\u4f9d\u7136\u5b58\u5728\u3002<\/p>\n<p>\u672c\u6587\u89e3\u8bfb<\/p>\n<p>\u6d4b\u4e0d\u51c6&#xff0c;\u662f\u56e0\u4e3a\u88ab\u91c7\u6837\u7684\u5bf9\u8c61\u8fdc\u5c0f\u4e8e\u89c2\u6d4b\u8005\u81ea\u8eab&#xff0c;\u5b83\u7684\u65f6\u95f4\u6d41\u901f\u8fdc\u5feb\u4e8e\u89c2\u6d4b\u8005\u3002<\/p>\n<p>\u89c2\u6d4b\u8005\u4e0e\u88ab\u89c2\u6d4b\u5bf9\u8c61\u4e4b\u95f4\u5b58\u5728\u5c3a\u5ea6\u5dee\u3002\u5bf9\u8c61\u8fdc\u5c0f\u4e8e\u89c2\u6d4b\u8005\u65f6&#xff0c;\u5176\u5185\u7980\u53d8\u5316\u5468\u671f \u03c4_obj \u8fdc\u5c0f\u4e8e\u89c2\u6d4b\u8005\u81ea\u8eab\u7684\u7279\u5f81\u65f6\u95f4\u3002\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u5728\u89c2\u6d4b\u8005\u5b8c\u6210\u4e00\u6b21\u91c7\u6837\u7684\u8fd9\u6bb5\u65f6\u95f4\u91cc&#xff0c;\u5bf9\u8c61\u5df2\u7ecf\u53d8\u5316\u4e86\u8bb8\u591a\u6b21\u3002<\/p>\n<p>\u7531\u539f\u7406\u4e00&#xff0c;\u7c92\u5b50\u662f\u4e00\u56e2\u65cb\u8f6c\u7684\u80fd\u91cf\u3002\u5b83\u7684\u4f4d\u7f6e\u548c\u5b83\u7684\u8f6c\u901f&#xff0c;\u662f\u540c\u4e00\u56e2\u80fd\u91cf\u5728\u4e24\u79cd\u95ee\u6cd5\u4e0b\u7684\u4e24\u4e2a\u8bfb\u6570&#xff0c;\u4e8c\u8005\u5171\u7528\u540c\u4e00\u4efd\u80fd\u91cf\u3002<\/p>\n<p>\u4e8e\u662f\u8fd9\u4e00\u5bf9\u8bfb\u6570\u65e0\u6cd5\u540c\u65f6\u53d6\u51c6&#xff0c;\u5176\u539f\u56e0\u4e0d\u5728\u5bf9\u8c61&#xff0c;\u800c\u5728\u4e8c\u8005\u5171\u7528\u4e00\u4efd\u80fd\u91cf\u8fd9\u4e00\u4e8b\u5b9e&#xff0c;\u52a0\u4e0a\u5c3a\u5dee\u9020\u6210\u7684\u6d41\u901f\u5dee&#xff1a;<\/p>\n<ul>\n<li>\u8981\u63d0\u9ad8\u4f4d\u7f6e\u7684\u91c7\u6837\u7cbe\u5ea6&#xff0c;\u9700\u8981\u628a\u89c2\u6d4b\u7a97\u53e3\u6536\u7d27&#xff1b;\u7a97\u53e3\u4e00\u6536&#xff0c;\u5728\u8fd9\u6bb5\u7a97\u53e3\u5185\u5bf9\u8c61\u7684\u8f6c\u901f\u53d8\u5316\u88ab\u622a\u65ad&#xff0c;\u8f6c\u901f\u8bfb\u6570\u968f\u4e4b\u53d8\u7c97\u3002<\/li>\n<li>\u8981\u63d0\u9ad8\u8f6c\u901f\u7684\u91c7\u6837\u7cbe\u5ea6&#xff0c;\u9700\u8981\u8ba9\u5bf9\u8c61\u8dd1\u4e00\u6bb5&#xff1b;\u8dd1\u8fc7\u4e00\u6bb5&#xff0c;\u4f4d\u7f6e\u5c31\u6563\u4e86\u3002<\/li>\n<\/ul>\n<p>\u4e0d\u662f\u5bf9\u8c61\u672c\u8eab\u4e0d\u786e\u5b9a&#xff0c;\u662f\u8fd9\u4e24\u4e2a\u8bfb\u6570\u65e0\u6cd5\u5728\u540c\u4e00\u4efd\u80fd\u91cf\u4e0a\u540c\u65f6\u53d6\u51c6\u3002<\/p>\n<p>\u65e2\u6709\u7406\u8bba\u628a\u8be5\u4e0b\u754c\u5199\u4f5c\u5e38\u91cf \u210f\/2\u3002\u672c\u6587\u9884\u671f\u8be5\u4e0b\u754c\u968f\u89c2\u6d4b\u8005\u4e0e\u5bf9\u8c61\u4e4b\u95f4\u7684\u5c3a\u5dee\u53d8\u5316&#xff1a;\u5c3a\u5dee\u8d8a\u5927&#xff0c;\u5bf9\u8c61\u7684\u6d41\u901f\u76f8\u5bf9\u89c2\u6d4b\u8005\u8d8a\u5feb&#xff0c;\u7a97\u53e3\u5185\u53e0\u5165\u7684\u76f8\u4f4d\u8d8a\u591a&#xff0c;\u4e0b\u754c\u8d8a\u5927\u3002<\/p>\n<p>\u4f9d\u636e&#xff1a;\u539f\u7406\u4e00\u3001\u539f\u7406\u4e09\u3001\u539f\u7406\u4e03\u3002<\/p>\n<p>\u5bf9\u7167<\/p>\n<ul>\n<li>\u65e2\u6709\u8868\u8ff0&#xff1a;\u5bf9\u8c61\u5177\u6709\u5185\u7980\u7684\u4e0d\u786e\u5b9a\u6027&#xff0c;\u8be5\u4e0b\u754c\u4e3a\u5e38\u91cf \u210f\/2\u3002\u9700\u63a5\u53d7&#034;\u4e0d\u786e\u5b9a&#034;\u4e3a\u5bf9\u8c61\u672c\u8eab\u7684\u5c5e\u6027\u3002<\/li>\n<li>\u672c\u6587\u8868\u8ff0&#xff1a;\u5bf9\u8c61\u662f\u786e\u5b9a\u7684&#xff0c;\u4e0d\u786e\u5b9a\u6765\u81ea\u89c2\u6d4b\u8005\u4e0e\u5bf9\u8c61\u4e4b\u95f4\u7684\u5c3a\u5dee\u4e0e\u91c7\u6837\u7a97\u53e3\u3002\u4e0b\u754c\u968f\u89c2\u6d4b\u65b9\u5f0f\u6539\u53d8&#xff08;\u89c1 \u00a74.2&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u65e2\u6709\u8868\u8ff0\u9700\u8981\u628a&#034;\u4e0d\u786e\u5b9a&#034;\u7acb\u4e3a\u5bf9\u8c61\u7684\u4e00\u9879\u5c5e\u6027&#xff1b;\u672c\u6587\u8868\u8ff0\u4e0d\u9700\u8981\u4e3a\u5bf9\u8c61\u589e\u52a0\u5c5e\u6027&#xff0c;\u53ea\u9700\u4fdd\u7559\u539f\u7406\u4e09\u2014\u2014\u89c2\u6d4b\u7a97\u53e3\u6709\u9650\u3002<\/p>\n<hr \/>\n<h4>3.3 \u81ea\u65cb<\/h4>\n<p>\u5b83\u662f\u4ec0\u4e48<\/p>\n<p>1922 \u5e74 Stern\u2013Gerlach \u5b9e\u9a8c\u53d1\u73b0&#xff0c;\u94f6\u539f\u5b50\u675f\u5728\u975e\u5747\u5300\u78c1\u573a\u4e2d\u5206\u88c2\u6210\u4e24\u675f&#xff0c;\u800c\u975e\u8fde\u7eed\u5206\u5e03\u3002\u968f\u540e\u786e\u7acb&#xff1a;\u7535\u5b50\u5177\u6709\u81ea\u65cb\u89d2\u52a8\u91cf&#xff0c;\u5176\u81ea\u65cb\u91cf\u5b50\u6570 s &#061; 1\/2&#xff0c;\u5728\u4efb\u4e00\u65b9\u5411\u4e0a\u7684\u6295\u5f71\u53ea\u53d6 \u00b1\u210f\/2 \u4e24\u4e2a\u503c\u3002\u81ea\u65cb\u89d2\u52a8\u91cf\u7684\u5927\u5c0f\u4e3a<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">S&#061;s(s&#043;1)\u2009\u210f&#061;32\u210fS &#061; \\\\sqrt{s(s&#043;1)}\\\\,\\\\hbar &#061; \\\\frac{\\\\sqrt{3}}{2}\\\\hbar<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24em;vertical-align: -0.2561em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9839em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mord mathnormal\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -2.9439em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2561em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u210f<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2702em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.5842em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9072em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\">3<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8672em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1328em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\">\u210f<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u81ea\u65cb\u4e3a\u534a\u6574\u6570\u7684\u7c92\u5b50&#xff08;\u8d39\u7c73\u5b50&#xff09;\u670d\u4ece\u6ce1\u5229\u4e0d\u76f8\u5bb9\u539f\u7406&#xff0c;\u8fd9\u51b3\u5b9a\u4e86\u539f\u5b50\u7684\u58f3\u5c42\u7ed3\u6784\u3002<\/p>\n<p>\u5176\u4e2d\u4e00\u5904\u9700\u8981\u5982\u5b9e\u5199\u51fa&#xff1a;\u6ce2\u51fd\u6570\u5728\u7a7a\u95f4\u65cb\u8f6c 2\u03c0 \u4e4b\u540e\u53d8\u53f7&#xff0c;\u65cb\u8f6c 4\u03c0 \u624d\u56de\u5230\u539f\u72b6\u3002 \u5728\u6570\u5b66\u4e0a&#xff0c;\u8fd9\u7531 SU(2) \u5bf9 SO(3) \u7684\u53cc\u91cd\u8986\u76d6\u7ed9\u51fa\u3002\u65e2\u6709\u7406\u8bba\u901a\u5e38\u63a5\u53d7\u8fd9\u4e00\u4e8b\u5b9e&#xff0c;\u5e76\u628a\u81ea\u65cb\u91cf\u5b50\u6570\u4f5c\u4e3a\u4e00\u4e2a\u8f93\u5165\u7684\u53c2\u6570&#xff0c;\u4e0d\u5bf9\u5176\u53d6\u503c\u4f5c\u8fdb\u4e00\u6b65\u89e3\u91ca\u2014\u2014\u4e3a\u4ec0\u4e48\u662f 1\/2&#xff0c;\u800c\u4e0d\u662f\u522b\u7684\u6570&#xff0c;\u5728\u65e2\u6709\u6846\u67b6\u5185\u6ca1\u6709\u7b54\u6848&#xff0c;\u53ea\u80fd\u4f5c\u4e3a\u516c\u8bbe\u63a5\u53d7\u3002<\/p>\n<p>\u672c\u6587\u89e3\u8bfb<\/p>\n<p>\u534a\u6574\u6570\u81ea\u65cb&#xff0c;\u662f\u80fd\u91cf\u65cb\u8f6c\u5230\u67d0\u4e00\u8f6c\u901f\u540e\u9501\u5b9a\u6784\u578b\u7684\u5fc5\u7136\u7ed3\u679c\u3002<\/p>\n<p>\u7531\u539f\u7406\u4e00&#xff0c;\u7c92\u5b50\u662f\u4e00\u56e2\u65cb\u8f6c\u7684\u80fd\u91cf\u3002\u80fd\u91cf\u8f6c\u5230\u67d0\u4e00\u8f6c\u901f\u540e\u9501\u6210\u6784\u578b&#xff0c;\u6784\u578b\u7684\u65cb\u5411\u7ed9\u51fa\u7535\u8377&#xff08;\u89c1 \u00a71.1 \u7684\u6620\u5c04\u8868&#xff09;\u3002\u81ea\u65cb\u91cf\u5b50\u6570 s &#061; 1\/2 \u4e0d\u662f\u51ed\u7a7a\u8f93\u5165\u7684\u53c2\u6570&#xff0c;\u800c\u662f\u8fd9\u56e2\u80fd\u91cf\u5728\u9501\u5b9a\u6784\u578b\u65f6&#xff0c;\u5176\u65cb\u8f6c\u72b6\u6001\u4e0e\u7a7a\u95f4\u65cb\u8f6c\u4e4b\u95f4\u7684\u4e00\u79cd\u62d3\u6251\u5173\u7cfb\u3002<\/p>\n<p>\u5173\u952e\u5728\u4e8e&#xff1a;\u80fd\u91cf\u6784\u578b\u7684\u65cb\u8f6c&#xff0c;\u4e0e\u89c2\u6d4b\u8005\u6240\u5728\u7a7a\u95f4\u7684\u65cb\u8f6c&#xff0c;\u662f\u4e24\u5957\u4e0d\u540c\u7684\u65cb\u8f6c\u3002 \u6784\u578b\u81ea\u8eab\u7684\u65cb\u8f6c\u5468\u671f\u4e0e\u7a7a\u95f4\u65cb\u8f6c\u7684\u5468\u671f\u4e0d\u5fc5\u4e00\u81f4\u3002\u5f53\u6784\u578b\u65cb\u8f6c\u534a\u5468\u5373\u56de\u5230\u81ea\u8eab\u65f6&#xff0c;\u5b83\u5728\u7a7a\u95f4\u65cb\u8f6c 2\u03c0 \u4e4b\u4e0b\u8868\u73b0\u4e3a\u53d8\u53f7&#xff0c;\u65cb\u8f6c 4\u03c0 \u624d\u56de\u5230\u539f\u72b6\u2014\u2014\u8fd9\u6b63\u662f SU(2) \u5bf9 SO(3) \u53cc\u91cd\u8986\u76d6\u7684\u7269\u7406\u6765\u6e90\u3002<\/p>\n<p>\u4e8e\u662f\u534a\u6574\u6570\u4e0d\u9700\u8981\u5047\u8bbe&#xff1a;\u5b83\u662f\u80fd\u91cf\u9501\u5b9a\u6784\u578b\u65f6&#xff0c;\u6784\u578b\u65cb\u8f6c\u4e0e\u7a7a\u95f4\u65cb\u8f6c\u4e4b\u95f4\u76f8\u4f4d\u5173\u7cfb\u7684\u81ea\u7136\u7ed3\u679c\u3002 \u6784\u578b\u8f6c\u534a\u5708\u5c31\u4e0e\u81ea\u8eab\u91cd\u5408&#xff0c;\u89c2\u6d4b\u8005\u5374\u8981\u8f6c\u4e00\u6574\u5708\u624d\u80fd\u770b\u5230\u540c\u6837\u7684\u72b6\u6001\u2014\u2014\u8fd9\u4e2a&#034;\u5dee\u534a\u5708&#034;&#xff0c;\u5c31\u662f s &#061; 1\/2\u3002<\/p>\n<p>\u4f9d\u636e&#xff1a;\u539f\u7406\u4e00\u3001\u539f\u7406\u56db\u3002<\/p>\n<p>\u5bf9\u7167<\/p>\n<ul>\n<li>\u65e2\u6709\u8868\u8ff0&#xff1a;\u81ea\u65cb\u91cf\u5b50\u6570 s &#061; 1\/2 \u662f\u4e00\u4e2a\u8f93\u5165\u7684\u53c2\u6570&#xff0c;\u5176\u53d6\u503c\u4e0d\u4f5c\u89e3\u91ca&#xff1b;\u6ce2\u51fd\u6570\u65cb\u8f6c 2\u03c0 \u53d8\u53f7\u8fd9\u4e00\u4e8b\u5b9e\u7531 SU(2) \u5bf9 SO(3) \u7684\u53cc\u91cd\u8986\u76d6\u7ed9\u51fa&#xff0c;\u4f46\u8be5\u8986\u76d6\u672c\u8eab\u4e5f\u662f\u63a5\u53d7\u7684\u6570\u5b66\u4e8b\u5b9e&#xff0c;\u4e0d\u8ffd\u95ee\u5176\u7269\u7406\u6765\u6e90\u3002<\/li>\n<li>\u672c\u6587\u8868\u8ff0&#xff1a;s &#061; 1\/2 \u6765\u81ea\u80fd\u91cf\u9501\u5b9a\u6784\u578b\u65f6\u6784\u578b\u65cb\u8f6c\u4e0e\u7a7a\u95f4\u65cb\u8f6c\u7684\u76f8\u4f4d\u5dee\u3002\u6784\u578b\u8f6c\u534a\u5708\u5373\u4e0e\u81ea\u8eab\u91cd\u5408&#xff0c;\u6545\u7a7a\u95f4\u65cb\u8f6c 2\u03c0 \u8868\u73b0\u4e3a\u53d8\u53f7\u3002\u534a\u6574\u6570\u4e0d\u662f\u53c2\u6570&#xff0c;\u662f\u6784\u578b\u65cb\u8f6c\u7684\u5fc5\u7136\u7ed3\u679c\u3002<\/li>\n<\/ul>\n<hr \/>\n<h4>3.4 \u91cf\u5b50\u5316<\/h4>\n<p>\u5b83\u662f\u4ec0\u4e48<\/p>\n<p>\u539f\u5b50\u4e2d\u7684\u7535\u5b50\u53ea\u80fd\u5360\u636e\u4e00\u7cfb\u5217\u5206\u7acb\u7684\u80fd\u7ea7&#xff0c;\u8dc3\u8fc1\u65f6\u5438\u6536\u6216\u53d1\u5c04\u7684\u5149\u5b50\u9891\u7387\u7531\u4e24\u80fd\u7ea7\u4e4b\u5dee\u51b3\u5b9a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u0394E&#061;E2\u2212E1&#061;h\u03bd\\\\Delta E &#061; E_2 &#8211; E_1 &#061; h\\\\nu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0637em\">\u03bd<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u80fd\u7ea7\u5206\u7acb\u8fd9\u4e00\u4e8b\u5b9e\u7531\u6c22\u539f\u5b50\u5149\u8c31\u7684\u79bb\u6563\u8c31\u7ebf\u76f4\u63a5\u7ed9\u51fa\u3002\u73bb\u5c14\u6a21\u578b\u628a\u5b83\u89e3\u91ca\u4e3a\u89d2\u52a8\u91cf\u91cf\u5b50\u5316&#xff1a;L &#061; n\u210f\u3002\u91cf\u5b50\u529b\u5b66\u8fdb\u4e00\u6b65\u628a\u5b83\u5199\u6210\u859b\u5b9a\u8c14\u65b9\u7a0b\u5728\u675f\u7f1a\u6001\u4e0b\u7684\u672c\u5f81\u503c\u2014\u2014\u8fb9\u754c\u6761\u4ef6\u4f7f\u80fd\u91cf\u53ea\u80fd\u53d6\u4e00\u7cfb\u5217\u5206\u7acb\u503c\u3002<\/p>\n<p>\u672c\u6587\u89e3\u8bfb<\/p>\n<p>\u80fd\u7ea7\u5206\u7acb&#xff0c;\u662f\u80fd\u91cf\u9501\u5b9a\u6784\u578b\u65f6\u8f6c\u901f\u53ea\u80fd\u53d6\u67d0\u4e9b\u79bb\u6563\u503c\u7684\u76f4\u63a5\u540e\u679c\u3002<\/p>\n<p>\u7531\u539f\u7406\u4e00&#xff0c;\u7c92\u5b50\u662f\u4e00\u56e2\u65cb\u8f6c\u7684\u80fd\u91cf&#xff0c;\u80fd\u91cf\u8f6c\u5230\u67d0\u4e00\u8f6c\u901f\u540e\u9501\u6210\u6784\u578b\u3002\u6784\u578b\u8981\u7a33\u5b9a\u5b58\u5728&#xff0c;\u5176\u65cb\u8f6c\u5fc5\u987b\u81ea\u6d3d\u2014\u2014\u8f6c\u4e00\u5708\u56de\u5230\u81ea\u8eab\u65f6&#xff0c;\u76f8\u4f4d\u8981\u5bf9\u5f97\u4e0a\u3002\u8fd9\u4e2a\u81ea\u6d3d\u6761\u4ef6\u628a\u8f6c\u901f\u9650\u5236\u5728\u4e00\u7cfb\u5217\u5206\u7acb\u503c\u4e0a&#xff0c;\u800c\u4e0d\u662f\u8fde\u7eed\u53d6\u503c\u3002<\/p>\n<p>\u4e8e\u662f\u80fd\u7ea7\u4e0d\u662f\u5916\u52a0\u7684\u91cf\u5b50\u5316\u89c4\u5219&#xff0c;\u800c\u662f\u80fd\u91cf\u9501\u5b9a\u6784\u578b\u65f6&#xff0c;\u65cb\u8f6c\u81ea\u6d3d\u6761\u4ef6\u7684\u81ea\u7136\u7ed3\u679c\u3002 \u5206\u7acb\u8c31\u7ebf\u4e0d\u662f&#034;\u80fd\u91cf\u88ab\u91cf\u5b50\u5316\u4e86&#034;&#xff0c;\u662f&#034;\u80fd\u8f6c\u5f97\u7a33\u7684\u8f6c\u901f\u53ea\u6709\u90a3\u4e48\u51e0\u6863&#034;\u3002\u8f6c\u901f\u53d6\u5206\u7acb\u503c&#xff0c;\u80fd\u7ea7\u81ea\u7136\u5206\u7acb&#xff1b;\u8dc3\u8fc1\u65f6\u653e\u51fa\u7684\u80fd\u91cf\u5dee&#xff0c;\u5c31\u662f\u4e24\u6863\u8f6c\u901f\u4e4b\u95f4\u7684\u5dee\u3002<\/p>\n<p>\u4f9d\u636e&#xff1a;\u539f\u7406\u4e00\u3001\u539f\u7406\u56db\u3002<\/p>\n<p>\u5bf9\u7167<\/p>\n<ul>\n<li>\u65e2\u6709\u8868\u8ff0&#xff1a;\u91cf\u5b50\u5316\u662f\u5bf9\u8c61\u7684\u5185\u7980\u5c5e\u6027&#xff0c;\u7531\u859b\u5b9a\u8c14\u65b9\u7a0b\u7684\u8fb9\u754c\u6761\u4ef6\u7ed9\u51fa&#xff0c;\u4f5c\u4e3a\u57fa\u672c\u5047\u8bbe\u63a5\u53d7&#xff1b;\u4e3a\u4ec0\u4e48\u8fb9\u754c\u6761\u4ef6\u5bfc\u81f4\u5206\u7acb&#xff0c;\u4e0d\u518d\u8ffd\u95ee\u3002<\/li>\n<li>\u672c\u6587\u8868\u8ff0&#xff1a;\u91cf\u5b50\u5316\u6765\u81ea\u80fd\u91cf\u9501\u5b9a\u6784\u578b\u65f6\u7684\u65cb\u8f6c\u81ea\u6d3d\u6761\u4ef6\u3002\u8f6c\u901f\u53ea\u80fd\u53d6\u4f7f\u6784\u578b\u81ea\u6d3d\u7684\u5206\u7acb\u503c&#xff0c;\u80fd\u7ea7\u968f\u4e4b\u5206\u7acb\u3002\u91cf\u5b50\u5316\u4e0d\u662f\u89c4\u5219&#xff0c;\u662f\u65cb\u8f6c\u9501\u5b9a\u7684\u5fc5\u7136\u7ed3\u679c\u3002<\/li>\n<\/ul>\n<p>\u524d\u8005\u628a&#034;\u91cf\u5b50\u5316&#034;\u7acb\u4e3a\u4e00\u6761\u57fa\u672c\u5047\u8bbe&#xff1b;\u540e\u8005\u4e0d\u9700\u8981\u589e\u52a0\u5047\u8bbe&#xff0c;\u53ea\u9700\u4fdd\u7559\u539f\u7406\u4e00\u2014\u2014\u7c92\u5b50\u662f\u65cb\u8f6c\u9501\u5b9a\u7684\u80fd\u91cf\u6784\u578b\u3002<\/p>\n<hr \/>\n<h4>3.5 \u6ce2\u7c92\u4e8c\u8c61\u6027<\/h4>\n<p>\u5b83\u662f\u4ec0\u4e48<\/p>\n<p>\u7535\u5b50\u5728\u53cc\u7f1d\u5b9e\u9a8c\u4e2d\u8868\u73b0\u51fa\u5e72\u6d89\u56fe\u6837&#xff08;\u6ce2\u52a8\u6027&#xff09;&#xff0c;\u5728\u78b0\u649e\u5b9e\u9a8c\u4e2d\u53c8\u8868\u73b0\u4e3a\u5b9a\u57df\u7684\u70b9&#xff08;\u7c92\u5b50\u6027&#xff09;\u3002\u5149\u540c\u6837\u5982\u6b64&#xff1a;\u5e72\u6d89\u3001\u884d\u5c04\u663e\u793a\u6ce2\u52a8\u6027&#xff0c;\u5149\u7535\u6548\u5e94\u663e\u793a\u7c92\u5b50\u6027\u3002\u5fb7\u5e03\u7f57\u610f\u7ed9\u51fa\u7269\u8d28\u6ce2\u6ce2\u957f\u4e0e\u52a8\u91cf\u7684\u5173\u7cfb&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bb&#061;hp\\\\lambda &#061; \\\\frac{h}{p}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2519em;vertical-align: -0.8804em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8804em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u91cf\u5b50\u529b\u5b66\u628a\u8fd9\u4e00\u4e8c\u8c61\u6027\u7eb3\u5165\u6ce2\u51fd\u6570&#xff1a;\u7c92\u5b50\u7531\u6ce2\u51fd\u6570\u63cf\u8ff0&#xff0c;|\u03c8|\u00b2 \u7ed9\u51fa\u5728\u67d0\u5904\u627e\u5230\u5b83\u7684\u6982\u7387\u5bc6\u5ea6\u3002\u6ce2\u4e0e\u7c92\u5b50\u88ab\u7edf\u4e00\u4e3a\u540c\u4e00\u5bf9\u8c61\u7684\u4e24\u79cd\u8868\u73b0&#xff0c;\u4f46&#034;\u5b83\u5230\u5e95\u662f\u6ce2\u8fd8\u662f\u7c92\u5b50&#034;\u5728\u65e2\u6709\u6846\u67b6\u5185\u6ca1\u6709\u76f4\u89c2\u7b54\u6848\u3002<\/p>\n<p>\u672c\u6587\u89e3\u8bfb<\/p>\n<p>\u6ce2\u7c92\u4e8c\u8c61\u6027&#xff0c;\u662f\u540c\u4e00\u56e2\u65cb\u8f6c\u80fd\u91cf\u5728\u4e24\u79cd\u89c2\u6d4b\u7a97\u53e3\u4e0b\u7684\u4e24\u79cd\u8bfb\u6570\u3002<\/p>\n<p>\u7531\u539f\u7406\u4e00&#xff0c;\u7c92\u5b50\u662f\u4e00\u56e2\u65cb\u8f6c\u7684\u80fd\u91cf&#xff0c;\u9501\u6210\u6784\u578b\u3002\u8fd9\u56e2\u80fd\u91cf\u5728\u7a7a\u95f4\u4e2d\u6709\u5e7f\u5ef6&#xff08;\u573a\u7684\u4e00\u9762&#xff09;&#xff0c;\u53c8\u96c6\u4e2d\u5728\u4e00\u4e2a\u6784\u578b\u4e0a&#xff08;\u7c92\u5b50\u7684\u4e00\u9762&#xff09;\u3002\u5b83\u672c\u6765\u5c31\u662f\u4e24\u8005\u2014\u2014\u4e0d\u662f&#034;\u65e2\u662f\u6ce2\u53c8\u662f\u7c92\u5b50&#034;&#xff0c;\u662f\u5b83\u540c\u65f6\u5177\u6709\u5e7f\u5ef6\u4e0e\u96c6\u4e2d\u4e24\u4e2a\u9762&#xff0c;\u89c2\u6d4b\u95ee\u54ea\u4e00\u9762&#xff0c;\u5c31\u7b54\u54ea\u4e00\u9762\u3002<\/p>\n<ul>\n<li>\u95ee\u5e72\u6d89&#xff1a;\u89c2\u6d4b\u7a97\u53e3\u8986\u76d6\u591a\u4e2a\u6784\u578b\u5468\u671f&#xff0c;\u91c7\u5230\u7684\u662f\u591a\u4e2a\u76f8\u4f4d\u53e0\u5728\u4e00\u8d77\u7684\u5206\u5e03\u2014\u2014\u8868\u73b0\u4e3a\u6ce2\u3002<\/li>\n<li>\u95ee\u78b0\u649e&#xff1a;\u89c2\u6d4b\u7a97\u53e3\u538b\u5f97\u591f\u7a84&#xff0c;\u53ea\u591f\u5bb9\u7eb3\u4e00\u4e2a\u6784\u578b\u2014\u2014\u8868\u73b0\u4e3a\u7c92\u5b50\u3002<\/li>\n<\/ul>\n<p>\u4e8e\u662f\u6ce2\u4e0e\u7c92\u5b50\u4e0d\u662f\u5bf9\u8c61\u7684\u4e24\u79cd\u72b6\u6001&#xff0c;\u662f\u540c\u4e00\u56e2\u80fd\u91cf\u5728\u4e24\u79cd\u91c7\u6837\u7a97\u53e3\u4e0b\u7684\u4e24\u79cd\u8bfb\u6570\u3002 \u7a97\u53e3\u5bbd&#xff0c;\u770b\u5230\u6ce2&#xff1b;\u7a97\u53e3\u7a84&#xff0c;\u770b\u5230\u7c92\u5b50\u3002\u5bf9\u8c61\u672c\u8eab\u6ca1\u6709\u53d8&#xff0c;\u53d8\u7684\u662f\u89c2\u6d4b\u5173\u7cfb\u3002<\/p>\n<p>\u4f9d\u636e&#xff1a;\u539f\u7406\u4e00\u3001\u539f\u7406\u4e09\u3001\u539f\u7406\u4e03\u3002<\/p>\n<p>\u5bf9\u7167<\/p>\n<ul>\n<li>\u65e2\u6709\u8868\u8ff0&#xff1a;\u5bf9\u8c61\u540c\u65f6\u5177\u6709\u6ce2\u4e0e\u7c92\u5b50\u4e24\u79cd\u5c5e\u6027&#xff0c;\u4e8c\u8005\u7531\u6ce2\u51fd\u6570\u7edf\u4e00&#xff1b;\u4f46&#034;\u4e3a\u4ec0\u4e48\u662f\u4e8c\u8c61&#034;\u4f5c\u4e3a\u57fa\u672c\u4e8b\u5b9e\u63a5\u53d7&#xff0c;\u4e0d\u518d\u8ffd\u95ee\u3002<\/li>\n<li>\u672c\u6587\u8868\u8ff0&#xff1a;\u5bf9\u8c61\u662f\u4e00\u56e2\u6709\u5e7f\u5ef6\u53c8\u96c6\u4e2d\u7684\u65cb\u8f6c\u80fd\u91cf\u3002\u6ce2\u4e0e\u7c92\u5b50\u662f\u540c\u4e00\u5bf9\u8c61\u5728\u5bbd\u7a84\u4e24\u79cd\u91c7\u6837\u7a97\u53e3\u4e0b\u7684\u4e24\u79cd\u8bfb\u6570\u3002\u4e8c\u8c61\u6027\u4e0d\u662f\u5bf9\u8c61\u7684\u5c5e\u6027&#xff0c;\u662f\u89c2\u6d4b\u7a97\u53e3\u7684\u4e24\u79cd\u53d6\u6cd5\u3002<\/li>\n<\/ul>\n<p>\u524d\u8005\u9700\u8981\u628a&#034;\u4e8c\u8c61&#034;\u7acb\u4e3a\u5bf9\u8c61\u7684\u5185\u7980\u5c5e\u6027&#xff1b;\u540e\u8005\u4e0d\u9700\u8981\u4e3a\u5bf9\u8c61\u589e\u52a0\u5c5e\u6027&#xff0c;\u53ea\u9700\u4fdd\u7559\u539f\u7406\u4e09\u2014\u2014\u89c2\u6d4b\u7a97\u53e3\u6709\u9650\u3002<\/p>\n<hr \/>\n<h4>3.6 \u91cf\u5b50\u96a7\u7a7f<\/h4>\n<p>\u5b83\u662f\u4ec0\u4e48<\/p>\n<p>\u4e00\u4e2a\u80fd\u91cf\u4f4e\u4e8e\u52bf\u5792\u9ad8\u5ea6\u7684\u7c92\u5b50&#xff0c;\u4ecd\u6709\u4e00\u5b9a\u6982\u7387\u7a7f\u8fc7\u52bf\u5792\u3002\u7ecf\u5178\u529b\u5b66\u4e2d\u8fd9\u662f\u4e0d\u53ef\u80fd\u7684\u2014\u2014\u7c92\u5b50\u80fd\u91cf\u4e0d\u8db3&#xff0c;\u5230\u4e0d\u4e86\u52bf\u5792\u53e6\u4e00\u4fa7\u3002\u91cf\u5b50\u529b\u5b66\u4e2d&#xff0c;\u6ce2\u51fd\u6570\u5728\u52bf\u5792\u5185\u6307\u6570\u8870\u51cf\u4f46\u4e0d\u4e3a\u96f6&#xff0c;\u6545\u7c92\u5b50\u6709\u4e00\u5b9a\u6982\u7387\u51fa\u73b0\u5728\u52bf\u5792\u53e6\u4e00\u4fa7\u3002\u96a7\u7a7f\u6982\u7387\u968f\u52bf\u5792\u5bbd\u5ea6\u4e0e\u9ad8\u5ea6\u6307\u6570\u4e0b\u964d&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">T\u2248e\u22122\u03badT \\\\approx e^{-2\\\\kappa d}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8991em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mathnormal mtight\">\u03ba<\/span><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d \u03ba \u7531\u52bf\u5792\u9ad8\u5ea6\u4e0e\u7c92\u5b50\u80fd\u91cf\u4e4b\u5dee\u51b3\u5b9a&#xff0c;d \u4e3a\u52bf\u5792\u5bbd\u5ea6\u3002\u626b\u63cf\u96a7\u9053\u663e\u5fae\u955c\u3001\u03b1 \u8870\u53d8\u90fd\u4f9d\u8d56\u8fd9\u4e00\u6548\u5e94\u3002<\/p>\n<p>\u672c\u6587\u89e3\u8bfb<\/p>\n<p>\u96a7\u7a7f&#xff0c;\u662f\u80fd\u91cf\u5728\u6784\u578b\u5207\u6362\u7684\u95f4\u9699\u91cc&#xff0c;\u4ece\u52bf\u5792\u4e00\u4fa7\u6d41\u5230\u53e6\u4e00\u4fa7\u3002<\/p>\n<p>\u7531\u539f\u7406\u4e00&#xff0c;\u7c92\u5b50\u662f\u4e00\u56e2\u65cb\u8f6c\u7684\u80fd\u91cf&#xff0c;\u4e0d\u662f\u5b9e\u5fc3\u5c0f\u7403\u3002\u5b83\u6ca1\u6709\u786c\u8fb9\u754c&#xff0c;\u5411\u5916\u8fde\u7eed\u7a00\u8584&#xff08;\u89c1 \u00a71.3 \u63a8\u8bba&#xff09;\u3002\u6240\u8c13&#034;\u52bf\u5792&#034;&#xff0c;\u662f\u53e6\u4e00\u56e2\u80fd\u91cf\u5f62\u6210\u7684\u3001\u5bc6\u5ea6\u8f83\u9ad8\u7684\u533a\u57df\u3002\u7c92\u5b50\u8fd9\u56e2\u80fd\u91cf\u649e\u4e0a\u53bb&#xff0c;\u4e0d\u662f\u649e\u5728\u5899\u4e0a&#xff0c;\u662f\u4e24\u56e2\u80fd\u91cf\u76f8\u9047\u3002<\/p>\n<p>\u5173\u952e\u5728\u4e8e&#xff1a;\u7c92\u5b50\u5728\u6784\u578b\u4e4b\u95f4\u4ee5\u5468\u671f \u03c4_obj \u5207\u6362\u3002\u5728\u5207\u6362\u7684\u95f4\u9699\u91cc&#xff0c;\u5b83\u7684\u80fd\u91cf\u5206\u5e03\u662f\u5f00\u653e\u7684\u3001\u6d41\u52a8\u7684\u2014\u2014\u4e00\u90e8\u5206\u80fd\u91cf\u53ef\u4ee5\u7ed5\u8fc7\u6216\u6e17\u8fc7\u52bf\u5792\u7684\u8584\u5f31\u5904&#xff0c;\u5728\u53e6\u4e00\u4fa7\u91cd\u65b0\u805a\u6210\u6784\u578b\u3002\u89c2\u6d4b\u8005\u91c7\u4e00\u6b21\u6837&#xff0c;\u770b\u5230\u7684\u662f&#034;\u7c92\u5b50\u5728\u52bf\u5792\u53e6\u4e00\u4fa7&#034;\u2014\u2014\u4e0d\u662f\u5b83\u7a7f\u8fc7\u4e86\u5899&#xff0c;\u662f\u5b83\u7684\u4e00\u90e8\u5206\u80fd\u91cf\u5728\u5207\u6362\u95f4\u9699\u91cc\u6d41\u4e86\u8fc7\u53bb&#xff0c;\u91cd\u65b0\u9501\u6210\u4e86\u6784\u578b\u3002<\/p>\n<p>\u4e8e\u662f\u96a7\u7a7f\u4e0d\u9700\u8981\u5047\u8bbe&#034;\u7c92\u5b50\u540c\u65f6\u51fa\u73b0\u5728\u4e24\u4fa7&#034;&#xff1a;\u5b83\u662f\u80fd\u91cf\u5728\u6784\u578b\u5207\u6362\u95f4\u9699\u91cc\u7684\u6d41\u52a8&#xff0c;\u52a0\u4e0a\u89c2\u6d4b\u7a97\u53e3\u5bf9\u4f4d\u7f6e\u7684\u6a21\u7cca\u3002 \u52bf\u5792\u8d8a\u5bbd\u3001\u8d8a\u9ad8&#xff0c;\u80fd\u6e17\u8fc7\u53bb\u7684\u4efd\u989d\u8d8a\u5c0f&#xff0c;\u6982\u7387\u8d8a\u4f4e\u2014\u2014\u8fd9\u4e0e\u6307\u6570\u8870\u51cf\u4e00\u81f4\u3002<\/p>\n<p>\u4f9d\u636e&#xff1a;\u539f\u7406\u4e00\u3001\u539f\u7406\u4e09\u3001\u539f\u7406\u4e03\u3002<\/p>\n<p>\u5bf9\u7167<\/p>\n<ul>\n<li>\u65e2\u6709\u8868\u8ff0&#xff1a;\u7c92\u5b50\u4ee5\u6982\u7387\u7a7f\u8fc7\u52bf\u5792&#xff0c;\u6ce2\u51fd\u6570\u5728\u52bf\u5792\u5185\u4e0d\u4e3a\u96f6&#xff1b;&#034;\u4e3a\u4ec0\u4e48\u80fd\u7a7f&#034;\u4f5c\u4e3a\u91cf\u5b50\u529b\u5b66\u7684\u63a8\u8bba\u63a5\u53d7&#xff0c;\u4e0d\u8ffd\u95ee\u5176\u673a\u5236\u3002<\/li>\n<li>\u672c\u6587\u8868\u8ff0&#xff1a;\u7c92\u5b50\u662f\u4e00\u56e2\u5f00\u653e\u6d41\u52a8\u7684\u80fd\u91cf&#xff0c;\u5728\u6784\u578b\u5207\u6362\u95f4\u9699\u91cc\u90e8\u5206\u80fd\u91cf\u6e17\u8fc7\u52bf\u5792&#xff0c;\u5728\u53e6\u4e00\u4fa7\u91cd\u65b0\u9501\u6210\u6784\u578b\u3002\u96a7\u7a7f\u662f\u80fd\u91cf\u6d41\u52a8\u7684\u7ed3\u679c&#xff0c;\u4e0d\u662f\u7c92\u5b50&#034;\u7a7f\u5899&#034;\u3002<\/li>\n<\/ul>\n<p>\u524d\u8005\u9700\u8981\u63a5\u53d7&#034;\u7c92\u5b50\u53ef\u4ee5\u51fa\u73b0\u5728\u7ecf\u5178\u4e0a\u4e0d\u53ef\u80fd\u7684\u4f4d\u7f6e&#034;\u8fd9\u4e00\u4e8b\u5b9e&#xff1b;\u540e\u8005\u4e0d\u9700\u8981&#xff0c;\u53ea\u9700\u4fdd\u7559\u539f\u7406\u4e00\u2014\u2014\u7c92\u5b50\u662f\u5f00\u653e\u6d41\u52a8\u7684\u80fd\u91cf\u6784\u578b\u3002<\/p>\n<hr \/>\n<h4>3.7 \u771f\u7a7a\u6da8\u843d<\/h4>\n<p>\u5b83\u662f\u4ec0\u4e48<\/p>\n<p>\u91cf\u5b50\u573a\u8bba\u4e2d&#xff0c;\u771f\u7a7a\u5e76\u975e\u7a7a\u65e0\u4e00\u7269&#xff0c;\u800c\u662f\u5145\u6ee1\u865a\u7c92\u5b50\u5bf9\u7684\u4e0d\u65ad\u4ea7\u751f\u4e0e\u6e6e\u706d\u3002\u6d77\u68ee\u5821\u4e0d\u786e\u5b9a\u6027\u5173\u7cfb\u5141\u8bb8\u5728\u6781\u77ed\u65f6\u95f4\u5185&#034;\u501f&#034;\u51fa\u80fd\u91cf \u0394E&#xff0c;\u53ea\u8981 \u0394E\u00b7\u0394t \u2264 \u210f\/2\u3002\u5361\u897f\u7c73\u5c14\u6548\u5e94\u2014\u2014\u4e24\u5757\u8d34\u8fd1\u7684\u91d1\u5c5e\u677f\u4e4b\u95f4\u5b58\u5728\u5438\u5f15\u529b\u2014\u2014\u88ab\u89c6\u4e3a\u771f\u7a7a\u6da8\u843d\u7684\u53ef\u89c2\u6d4b\u540e\u679c\u3002<\/p>\n<p>\u672c\u6587\u89e3\u8bfb<\/p>\n<p>\u771f\u7a7a\u6da8\u843d&#xff0c;\u662f\u771f\u7a7a\u80fd\u91cf\u573a\u81ea\u8eab\u7684\u6d41\u52a8\u4e0e\u541e\u5410&#xff0c;\u4e0d\u662f&#034;\u501f&#034;\u80fd\u91cf\u3002<\/p>\n<p>\u7531\u539f\u7406\u4e00&#xff0c;\u771f\u7a7a\u5e76\u975e\u65e0\u7269&#xff0c;\u800c\u662f\u80fd\u91cf\u5904\u4e8e\u6781\u7a00\u8584\u72b6\u6001\u7684\u573a&#xff0c;\u5176\u80fd\u91cf\u5bc6\u5ea6\u4e0d\u4e3a\u96f6\u3002\u8fd9\u4e2a\u573a\u4e0d\u662f\u9759\u6b62\u7684&#xff0c;\u5b83\u5728\u6d41\u52a8\u3001\u5728\u8d77\u4f0f\u2014\u2014\u5c31\u50cf\u6c34\u9762\u4e0d\u4f1a\u7edd\u5bf9\u5e73\u9759\u3002\u6240\u8c13&#034;\u865a\u7c92\u5b50\u5bf9\u7684\u4ea7\u751f\u4e0e\u6e6e\u706d&#034;&#xff0c;\u662f\u771f\u7a7a\u80fd\u91cf\u573a\u5c40\u90e8\u7684\u5bc6\u5ea6\u8d77\u4f0f&#xff1a;\u4e00\u5904\u9686\u8d77&#xff0c;\u4e00\u5904\u51f9\u9677&#xff0c;\u968f\u5373\u53c8\u6d41\u5e73\u3002<\/p>\n<p>\u4e8e\u662f\u4e0d\u9700\u8981&#034;\u501f&#034;\u80fd\u91cf&#xff1a;\u771f\u7a7a\u672c\u6765\u5c31\u6709\u80fd\u91cf&#xff0c;\u6da8\u843d\u662f\u5b83\u81ea\u8eab\u7684\u8fd0\u52a8\u3002 \u5361\u897f\u7c73\u5c14\u6548\u5e94\u4e0d\u662f\u865a\u7c92\u5b50&#034;\u63a8&#034;\u51fa\u6765\u7684&#xff0c;\u662f\u4e24\u677f\u4e4b\u95f4\u4e0e\u4e24\u677f\u4e4b\u5916\u7684\u80fd\u91cf\u573a\u5bc6\u5ea6\u4e0d\u540c&#xff0c;\u538b\u529b\u5dee\u628a\u677f\u538b\u62e2\u3002\u771f\u7a7a\u4e0d\u662f\u7a7a\u7684&#xff0c;\u662f\u6781\u7a00\u8584\u7684\u80fd\u91cf\u573a\u5728\u8d77\u4f0f\u3002<\/p>\n<p>\u4f9d\u636e&#xff1a;\u539f\u7406\u4e00\u3002<\/p>\n<p>\u5bf9\u7167<\/p>\n<ul>\n<li>\u65e2\u6709\u8868\u8ff0&#xff1a;\u771f\u7a7a\u6da8\u843d\u662f\u865a\u7c92\u5b50\u5bf9\u7684\u4ea7\u751f\u4e0e\u6e6e\u706d&#xff0c;\u9700\u8981\u501f\u52a9\u4e0d\u786e\u5b9a\u6027\u5173\u7cfb&#034;\u501f&#034;\u80fd\u91cf&#xff1b;\u771f\u7a7a\u88ab\u63cf\u8ff0\u4e3a\u5145\u6ee1\u77ac\u65f6\u6d3b\u52a8\u7684&#034;\u91cf\u5b50\u6ce1\u6cab&#034;\u3002<\/li>\n<li>\u672c\u6587\u8868\u8ff0&#xff1a;\u771f\u7a7a\u662f\u6781\u7a00\u8584\u7684\u80fd\u91cf\u573a&#xff0c;\u6da8\u843d\u662f\u5b83\u81ea\u8eab\u7684\u5bc6\u5ea6\u8d77\u4f0f\u4e0e\u6d41\u52a8\u3002\u4e0d\u9700\u8981&#034;\u501f&#034;\u80fd\u91cf&#xff0c;\u4e5f\u4e0d\u9700\u8981\u865a\u7c92\u5b50\u5bf9\u2014\u2014\u771f\u7a7a\u672c\u6765\u5c31\u6709\u80fd\u91cf&#xff0c;\u5b83\u5728\u6d41\u53d8\u3002<\/li>\n<\/ul>\n<p>\u524d\u8005\u9700\u8981\u5047\u8bbe\u771f\u7a7a\u4e2d\u6709\u865a\u7c92\u5b50\u5bf9\u4e0d\u65ad\u4ea7\u751f\u6e6e\u706d&#xff1b;\u540e\u8005\u4e0d\u9700\u8981&#xff0c;\u53ea\u9700\u4fdd\u7559\u539f\u7406\u4e00\u2014\u2014\u771f\u7a7a\u662f\u80fd\u91cf&#xff0c;\u53ea\u662f\u6781\u7a00\u8584\u3002<\/p>\n<hr \/>\n<h4>3.8 \u91cf\u5b50\u7ea0\u7f20<\/h4>\n<p>\u5b83\u662f\u4ec0\u4e48<\/p>\n<p>\u4e24\u4e2a\u7c92\u5b50\u53d1\u751f\u76f8\u4e92\u4f5c\u7528\u540e&#xff0c;\u5176\u72b6\u6001\u4e0d\u518d\u72ec\u7acb\u63cf\u8ff0\u3002\u5bf9\u5176\u4e2d\u4e00\u4e2a\u7684\u6d4b\u91cf\u4f1a\u5373\u65f6\u786e\u5b9a\u53e6\u4e00\u4e2a\u7684\u72b6\u6001&#xff0c;\u65e0\u8bba\u4e8c\u8005\u76f8\u8ddd\u591a\u8fdc\u3002EPR \u4f6f\u8c2c\u6307\u51fa\u8fd9\u4e0e\u5b9a\u57df\u5b9e\u5728\u8bba\u51b2\u7a81&#xff1b;\u8d1d\u5c14\u4e0d\u7b49\u5f0f\u7ed9\u51fa\u53ef\u68c0\u9a8c\u7684\u5224\u636e&#xff0c;\u5b9e\u9a8c&#xff08;\u5982 Aspect \u5b9e\u9a8c&#xff09;\u8868\u660e\u91cf\u5b50\u529b\u5b66\u7684\u9884\u8a00\u6210\u7acb\u2014\u2014\u7ea0\u7f20\u5173\u8054\u4e0d\u80fd\u7528&#034;\u4e8b\u5148\u7ea6\u5b9a\u597d\u7684\u9690\u85cf\u53d8\u91cf&#034;\u89e3\u91ca\u3002<\/p>\n<p>\u672c\u6587\u89e3\u8bfb<\/p>\n<p>\u7ea0\u7f20&#xff0c;\u662f\u4e24\u4e2a\u6784\u578b\u5171\u4eab\u540c\u4e00\u4efd\u80fd\u91cf&#xff0c;\u6d4b\u91cf\u4e00\u4e2a\u5c31\u662f\u6d4b\u91cf\u8fd9\u4efd\u80fd\u91cf\u7684\u4e00\u4e2a\u9762\u3002<\/p>\n<p>\u7531\u539f\u7406\u4e00&#xff0c;\u7c92\u5b50\u662f\u4e00\u56e2\u65cb\u8f6c\u7684\u80fd\u91cf\u3002\u4e24\u4e2a\u7c92\u5b50\u53d1\u751f\u76f8\u4e92\u4f5c\u7528\u65f6&#xff0c;\u5b83\u4eec\u4e0d\u662f\u4e24\u4e2a\u72ec\u7acb\u7684\u5b9e\u5fc3\u7403\u78b0\u4e86\u4e00\u4e0b&#xff0c;\u800c\u662f\u4e24\u56e2\u80fd\u91cf\u53d1\u751f\u4e86\u4ea4\u6362\u4e0e\u8026\u5408\u2014\u2014\u4e00\u90e8\u5206\u80fd\u91cf\u5728\u4e8c\u8005\u4e4b\u95f4\u6d41\u52a8\u3001\u5171\u4eab\u3002\u6b64\u540e\u5b83\u4eec\u4e0d\u518d\u662f\u4e24\u4e2a\u5b8c\u5168\u72ec\u7acb\u7684\u6784\u578b&#xff0c;\u800c\u662f\u540c\u4e00\u4efd\u80fd\u91cf\u5728\u4e24\u4e2a\u4f4d\u7f6e\u4e0a\u7684\u4e24\u4e2a\u9501\u5b9a\u7aef\u3002<\/p>\n<p>\u4e8e\u662f\u5bf9\u5176\u4e2d\u4e00\u4e2a\u7684\u6d4b\u91cf&#xff0c;\u6d4b\u7684\u662f\u8fd9\u4efd\u5171\u4eab\u80fd\u91cf\u7684\u4e00\u4e2a\u9762&#xff1b;\u8fd9\u4efd\u80fd\u91cf\u7684\u72b6\u6001\u786e\u5b9a\u4e86&#xff0c;\u53e6\u4e00\u4e2a\u7aef\u7684\u72b6\u6001\u968f\u4e4b\u786e\u5b9a\u3002\u4e0d\u662f\u4fe1\u606f\u8d85\u5149\u901f\u4f20\u9012\u4e86&#xff0c;\u662f\u4e8c\u8005\u672c\u6765\u5c31\u5728\u540c\u4e00\u4efd\u80fd\u91cf\u4e0a&#xff0c;\u6d4b\u91cf\u4e00\u4e2a\u5c31\u662f\u8bfb\u53d6\u8fd9\u4efd\u80fd\u91cf\u7684\u6574\u4f53\u72b6\u6001\u3002<\/p>\n<p>\u4f9d\u636e&#xff1a;\u539f\u7406\u4e00\u3002<\/p>\n<p>\u5bf9\u7167<\/p>\n<ul>\n<li>\u65e2\u6709\u8868\u8ff0&#xff1a;\u7ea0\u7f20\u662f\u91cf\u5b50\u6001\u7684\u975e\u5b9a\u57df\u5173\u8054&#xff0c;\u6d4b\u91cf\u4e00\u4e2a\u7c92\u5b50\u5373\u65f6\u786e\u5b9a\u53e6\u4e00\u4e2a&#xff1b;\u8d1d\u5c14\u5b9e\u9a8c\u8868\u660e\u4e0d\u80fd\u7528\u5b9a\u57df\u9690\u53d8\u91cf\u89e3\u91ca&#xff0c;\u4f46&#034;\u4e3a\u4ec0\u4e48\u975e\u5b9a\u57df&#034;\u4f5c\u4e3a\u57fa\u672c\u4e8b\u5b9e\u63a5\u53d7\u3002<\/li>\n<li>\u672c\u6587\u8868\u8ff0&#xff1a;\u7ea0\u7f20\u662f\u4e24\u4e2a\u6784\u578b\u5171\u4eab\u540c\u4e00\u4efd\u80fd\u91cf\u3002\u6d4b\u91cf\u4e00\u4e2a\u5c31\u662f\u8bfb\u53d6\u8fd9\u4efd\u5171\u4eab\u80fd\u91cf\u7684\u72b6\u6001&#xff0c;\u53e6\u4e00\u4e2a\u7aef\u968f\u4e4b\u786e\u5b9a\u3002\u4e0d\u9700\u8981\u8d85\u5149\u901f\u4f20\u9012&#xff0c;\u4e5f\u4e0d\u9700\u8981\u9690\u53d8\u91cf\u2014\u2014\u4e8c\u8005\u672c\u6765\u5c31\u5728\u540c\u4e00\u4efd\u80fd\u91cf\u4e0a\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>4 \u4e09\u6761\u53ef\u7531\u89c2\u6d4b\u68c0\u9a8c\u7684\u540e\u679c<\/h3>\n<p>\u7b2c 3 \u8282\u7ed9\u51fa\u7684\u662f\u4e24\u79cd\u8868\u8ff0\u7684\u5e76\u5217\u3002\u672c\u8282\u628a\u672c\u6587\u7684\u8868\u8ff0\u63a8\u5230\u53ef\u68c0\u9a8c\u5904&#xff1a;\u4e09\u6761\u540e\u679c&#xff0c;\u6bcf\u4e00\u6761\u90fd\u7ed9\u51fa\u5177\u4f53\u7684\u5b9e\u9a8c\u8bbe\u7f6e\u3001\u9884\u671f\u7684\u89c2\u6d4b\u7ed3\u679c&#xff0c;\u4ee5\u53ca\u4e0e\u65e2\u6709\u7406\u8bba\u9884\u8a00\u7684\u5dee\u5f02\u70b9\u3002\u4e09\u6761\u5206\u522b\u5bf9\u5e94\u539f\u7406\u516b&#xff08;\u7a97\u53e3\u6539\u53d8&#xff0c;\u5206\u5e03\u968f\u4e4b\u6539\u53d8&#xff09;\u3001\u00a73.2 \u7684\u9884\u671f&#xff08;\u6d4b\u4e0d\u51c6\u4e0b\u754c\u968f\u5c3a\u5dee\u53d8\u5316&#xff09;\u3001\u4ee5\u53ca \u00a73.8 \u7684\u5171\u4eab\u80fd\u91cf\u6846\u67b6&#xff08;\u7ea0\u7f20\u5173\u8054\u7684\u53ef\u68c0\u9a8c\u7279\u5f81&#xff09;\u3002<\/p>\n<h4>4.1 \u6539\u53d8\u89c2\u6d4b\u7a97\u53e3&#xff0c;\u5206\u5e03\u5f62\u5f0f\u968f\u4e4b\u6539\u53d8<\/h4>\n<p>\u5bf9\u5e94&#xff1a;\u539f\u7406\u516b\u3002<\/p>\n<p>\u5b9e\u9a8c\u8bbe\u7f6e<\/p>\n<p>\u5bf9\u540c\u4e00\u7c7b\u5fae\u89c2\u5bf9\u8c61&#xff08;\u5982\u5355\u5149\u5b50\u6e90\u53d1\u51fa\u7684\u5149\u5b50\u3001\u6216\u5355\u4e2a\u56da\u7981\u79bb\u5b50&#xff09;&#xff0c;\u56fa\u5b9a\u5176\u5185\u7980\u53d8\u5316\u5468\u671f \u03c4_obj \u4e0d\u53d8&#xff0c;\u53ea\u6539\u53d8\u89c2\u6d4b\u7a97\u53e3 \u0394t \u91c7\u6837\u3002\u5177\u4f53\u505a\u6cd5&#xff1a;\u7528\u53ef\u8c03\u95e8\u63a7\u7684\u63a2\u6d4b\u5668&#xff0c;\u628a\u5355\u6b21\u91c7\u6837\u7684\u79ef\u5206\u7a97\u53e3\u4ece\u8fdc\u5c0f\u4e8e \u03c4_obj \u9010\u6b65\u62c9\u957f\u5230\u8fdc\u5927\u4e8e \u03c4_obj\u3002\u5728\u6bcf\u4e00\u6863\u7a97\u53e3\u4e0b&#xff0c;\u8bb0\u5f55\u5927\u91cf\u5355\u6b21\u8bfb\u6570&#xff0c;\u7edf\u8ba1\u5176\u5206\u5e03\u5f62\u5f0f\u3002<\/p>\n<p>\u9884\u671f\u89c2\u6d4b\u7ed3\u679c<\/p>\n<ul>\n<li>\u5f53 \u0394t \u91c7\u6837 \u8fdc\u5c0f\u4e8e \u03c4_obj&#xff08;N \u2264 1\/2&#xff09;\u65f6&#xff0c;\u8bfb\u6570\u6536\u655b\u4e3a\u786e\u5b9a\u503c\u2014\u2014\u6bcf\u6b21\u91c7\u5230\u7684\u90fd\u662f\u540c\u4e00\u4e2a\u6784\u578b&#xff0c;\u5206\u5e03\u8d8b\u8fd1\u4e8e\u5355\u70b9\u3002<\/li>\n<li>\u5f53 \u0394t \u91c7\u6837 \u9010\u6e10\u62c9\u957f\u3001\u8d8a\u8fc7 N &#061; 1\/2 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|a|\u00b2\u3001|b|\u00b2&#xff09;\u4e0d\u53d8\u3002<\/li>\n<li>\u672c\u6587&#xff1a;\u5206\u5e03\u5f62\u5f0f\u662f\u89c2\u6d4b\u7a97\u53e3\u4e0e\u5bf9\u8c61\u5468\u671f\u4e4b\u6bd4\u7684\u51fd\u6570\u3002\u540c\u4e00\u5bf9\u8c61\u3001\u540c\u4e00\u72b6\u6001&#xff0c;\u53ea\u8981\u6539\u7a97\u53e3&#xff0c;\u5206\u5e03\u5c31\u53d8\u3002 \u8fd9\u662f\u539f\u7406\u516b\u7684\u76f4\u63a5\u68c0\u9a8c\u2014\u2014\u5206\u5e03\u5f62\u5f0f\u7684\u6539\u53d8\u4e0d\u8574\u542b\u5bf9\u8c61\u672c\u8eab\u7684\u6539\u53d8\u3002<\/li>\n<\/ul>\n<h4>4.2 \u6d4b\u4e0d\u51c6\u4e0b\u754c\u968f\u5c3a\u5dee\u53d8\u5316<\/h4>\n<p>\u5bf9\u5e94&#xff1a;\u00a73.2 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