{"id":30803,"date":"2021-04-26T13:00:33","date_gmt":"2021-04-26T13:00:33","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30803"},"modified":"2025-01-01T23:46:25","modified_gmt":"2025-01-01T23:46:25","slug":"%e7%8e%bb%e5%b0%94%e5%85%b9%e6%9b%bc%e5%88%86%e5%b8%83%e5%9c%a8%e6%ad%a3%e5%88%99%e7%b3%bb%e7%bb%bc%e4%b8%ad","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e7%8e%bb%e5%b0%94%e5%85%b9%e6%9b%bc%e5%88%86%e5%b8%83%e5%9c%a8%e6%ad%a3%e5%88%99%e7%b3%bb%e7%bb%bc%e4%b8%ad\/","title":{"rendered":"\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u5728\u6b63\u5219\u7cfb\u7efc\u4e2d"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\t\ttext-align: center;\n\t}\n<\/style>\n<h1>\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u5728\u6b63\u5219\u7cfb\u7efc\u4e2d<\/h1>\n<p style=\"text-align:center;\">\u70ed\u529b\u5b66\u63ed\u793a\u4e86\u7269\u7406\u7cfb\u7edf\u5982\u4f55\u8fbe\u5230\u5e73\u8861\uff0c\u4ee5\u53ca\u80fd\u91cf\u548c\u6982\u7387\u5982\u4f55\u51b3\u5b9a\u5176\u884c\u4e3a\u3002\u5728\u672c\u8bfe\u7a0b\u4e2d\uff0c\u6211\u4eec\u5c06\u6df1\u5165\u63a2\u8ba8\u6b63\u5219\u7cfb\u7efc\u548c\u73bb\u5c14\u5179\u66fc\u5206\u5e03\uff0c\u8fd9\u662f\u7406\u89e3\u5316\u5b66\u53cd\u5e94\u548c\u590d\u6742\u7cfb\u7edf\u5e73\u8861\u7684\u57fa\u672c\u5de5\u5177\u3002\u60a8\u5c06\u53d1\u73b0\u8fd9\u4e9b\u601d\u60f3\u5982\u4f55\u5c06\u6e29\u5ea6\u4e0e\u79e9\u5e8f\u548c\u6df7\u4e71\u8054\u7cfb\u8d77\u6765\uff0c\u4ece\u800c\u9884\u6d4b\u770b\u4f3c\u4e0d\u53ef\u9884\u6d4b\u7684\u884c\u4e3a\u3002<\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5b8c\u6210\u672c\u8bfe\u7a0b\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<li><strong>\u8bc6\u522b<\/strong>\u70ed\u529b\u5b66\u7cfb\u7efc\u7684\u7c7b\u578b\uff08\u5fae\u6b63\u5219\u7cfb\u7efc\u3001\u6b63\u5219\u7cfb\u7efc\u548c\u5de8\u6b63\u5219\u7cfb\u7efc\uff09\u3002<\/li>\n<li><strong>\u63a8\u5bfc<\/strong>\u57fa\u4e8e\u70ed\u529b\u5b66\u539f\u7406\u7684\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u3002<\/li>\n<li><strong>\u8ba1\u7b97<\/strong>\u4f7f\u7528\u5206\u914d\u51fd\u6570\u4e0e\u5fae\u89c2\u72b6\u6001\u76f8\u5173\u7684\u6982\u7387\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u5185\u5bb9\u76ee\u5f55<\/u>\uff1a<\/strong><br \/>\n<a href=\"#1\">\u70ed\u529b\u5b66\u4e2d\u7684\u7cfb\u7efc<\/a><br \/>\n<a href=\"#2\">\u73bb\u5c14\u5179\u66fc\u5206\u5e03<\/a><br \/>\n<a href=\"#3\">\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7684\u5e94\u7528<\/a><br \/>\n<a href=\"#4\">\u7ec3\u4e60<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ch1bjhU7k70\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p>\u70ed\u529b\u5b66\u6700\u6709\u7528\u7684\u6982\u5ff5\u5de5\u5177\u4e4b\u4e00\u662f\u201c\u7cfb\u7efc\u201d\u7684\u6982\u5ff5\u3002\u5728\u73b0\u6709\u7684\u591a\u79cd\u7cfb\u7efc\u4e2d\uff0c\u6b63\u5219\u7cfb\u7efc\u662f\u6700\u5e38\u7528\u7684\u7cfb\u7efc\u4e4b\u4e00\uff0c\u800c\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u6b63\u662f\u7531\u6b64\u63a8\u5bfc\u51fa\u6765\u7684\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u56de\u987e\u8fd9\u4e24\u4e2a\u6982\u5ff5\u3002<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u70ed\u529b\u5b66\u4e2d\u7684\u7cfb\u7efc<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=ch1bjhU7k70&amp;t=174s\" target=\"_blank\" rel=\"noopener\"><strong>\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u5df2\u7ecf\u4f7f\u7528\u6982\u7387<\/strong><\/a>\u6765\u63cf\u8ff0\u70ed\u529b\u5b66\u7cfb\u7edf\u3002\u6211\u4eec\u7684\u7814\u7a76\u91cd\u70b9\u662f\u60f3\u8c61\u6211\u4eec\u53ef\u4ee5\u91cd\u590d\u5b9e\u9a8c\u548c\u6d4b\u91cf\u65e0\u6570\u6b21\uff0c\u4ee5\u5f25\u8865\u6211\u4eec\u65e0\u6cd5\u63a7\u5236\u5176\u5fae\u89c2\u5c5e\u6027\uff08\u901a\u8fc7\u5fae\u89c2\u72b6\u6001\u63cf\u8ff0\uff09\u7684\u4e0d\u8db3\u3002\u53d7\u5230\u8fd9\u4e9b\u601d\u60f3\u7684\u542f\u53d1\uff0c<a href=\"https:\/\/zh.wikipedia.org\/wiki\/%E5%8A%A0%E5%8B%92%E8%A5%BF%C2%B7%E5%B0%94%E5%85%8B%E9%80%8A%C2%B7%E5%8A%A0%E5%8E%8B%E8%80%B6%C2%B7%E5%9F%BA%E5%B8%83%E6%96%AF\" rel=\"noopener, nofollow, noreferrer noopener\" target=\"_blank\">\u5409\u5e03\u65af<\/a>\u4e8e1878\u5e74\u5f15\u5165\u4e86\u201c\u7cfb\u7efc\u201d\u8fd9\u4e00\u6982\u5ff5\uff1a\u8fd9\u662f\u4e00\u79cd\u7406\u60f3\u5316\uff0c\u5c06\u7cfb\u7edf\u7684\u8bb8\u591a\u201c\u526f\u672c\u201d\u89c6\u4e3a\u6bcf\u4e00\u4e2a\u53ef\u80fd\u72b6\u6001\u7684\u4ee3\u8868\u3002\u5728\u70ed\u529b\u5b66\u4e2d\uff0c\u5b9a\u4e49\u4e86\u4e09\u79cd\u4e3b\u8981\u7c7b\u578b\u7684\u7cfb\u7efc\uff1a<\/p>\n<ol>\n<li><strong>\u5fae\u6b63\u5219\u7cfb\u7efc\uff1a<\/strong>\u4e00\u4e2a\u6240\u6709\u7cfb\u7edf\u90fd\u5177\u6709\u76f8\u540c\u56fa\u5b9a\u80fd\u91cf\u7684\u96c6\u5408\u3002<\/li>\n<li><strong>\u6b63\u5219\u7cfb\u7efc\uff1a<\/strong>\u4e00\u4e2a\u7cfb\u7edf\u96c6\u5408\uff0c\u5176\u4e2d\u6bcf\u4e2a\u7cfb\u7edf\u90fd\u53ef\u4ee5\u4e0e\u4e00\u4e2a\u5927\u70ed\u5e93\u4ea4\u6362\u80fd\u91cf\u3002\u6b63\u5982\u6211\u4eec\u5c06\u770b\u5230\u7684\uff0c\u8fd9\u786e\u5b9a\u4e86\uff08\u5e76\u5b9a\u4e49\u4e86\uff09\u7cfb\u7edf\u7684\u6e29\u5ea6\u3002<\/li>\n<li><strong>\u5de8\u6b63\u5219\u7cfb\u7efc\uff1a<\/strong>\u4e00\u4e2a\u7cfb\u7edf\u96c6\u5408\uff0c\u5176\u4e2d\u6bcf\u4e2a\u7cfb\u7edf\u90fd\u53ef\u4ee5\u4e0e\u4e00\u4e2a\u5927\u50a8\u5e93\u540c\u65f6\u4ea4\u6362\u7269\u8d28\uff08\u7c92\u5b50\uff09\u548c\u80fd\u91cf\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u7cfb\u7edf\u7684\u6e29\u5ea6\u548c\u5316\u5b66\u52bf\u5f97\u4ee5\u5b9a\u4e49\u3002<\/li>\n<\/ol>\n<h3>\u6b63\u5219\u7cfb\u7efc<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=ch1bjhU7k70&amp;t=362s\" target=\"_blank\" rel=\"noopener\"><strong>\u8ba9\u6211\u4eec\u8003\u8651\u4e24\u4e2a\u8026\u5408\u7cfb\u7edf<\/strong><\/a>\uff0c\u4f7f\u5b83\u4eec\u53ef\u4ee5\u4ea4\u6362\u80fd\u91cf\u3002\u4e0d\u8fc7\uff0c\u8fd9\u6b21\u6211\u4eec\u5c06\u5176\u4e2d\u4e00\u4e2a\u8bbe\u4e3a\u76f8\u5bf9\u4e8e\u53e6\u4e00\u4e2a\u975e\u5e38\u5927\u7684\u7cfb\u7edf\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a<strong>\u50a8\u5e93\u3001\u6e90<\/strong>\u6216<strong>\u70ed\u5e93\u3002<\/strong> \u8fd9\u4e2a\u50a8\u5e93\u662f\u5982\u6b64\u4e4b\u5927\uff0c\u4ee5\u81f3\u4e8e\u6211\u4eec\u53ef\u4ee5\u63d0\u53d6\u5927\u91cf\u80fd\u91cf\u800c\u4e0d\u4f1a\u6539\u53d8\u5176\u6e29\u5ea6\u3002\u50a8\u5e93\u4e2d\u80fd\u91cf\u91cf\u5b50\u7684\u91cd\u65b0\u6392\u5217\u65b9\u5f0f\u6570\u91cf\u56e0\u800c\u662f\u5de8\u5927\u7684\u3002\u53e6\u4e00\u4e2a\u7cfb\u7edf\u76f8\u8f83\u4e4b\u4e0b\u5f88\u5c0f\uff0c\u6211\u4eec\u5c06\u5176\u7b80\u5355\u5730\u79f0\u4e3a<strong>\u7cfb\u7edf\u3002<\/strong><\/p>\n<p>\u6211\u4eec\u5047\u8bbe\u7cfb\u7edf\u7684\u6bcf\u4e00\u4e2a\u5141\u8bb8\u80fd\u91cf\u90fd\u5bf9\u5e94\u4e00\u4e2a\u552f\u4e00\u7684\u5fae\u89c2\u72b6\u6001\uff0c\u56e0\u6b64\u7cfb\u7edf\u59cb\u7ec8\u5177\u6709 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega=1.<\/span> \u7684\u503c\u3002\u6b64\u5916\uff0c\u6211\u4eec\u4fdd\u6301\u8026\u5408\u7cfb\u7edf\u7684\u603b\u80fd\u91cf\u56fa\u5b9a\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">E.<\/span>\n<p><em>\u5982\u679c\u6211\u4eec\u5728\u6b64\u65f6\u505c\u6b62\u89c2\u5bdf\uff0c\u6211\u4eec\u4f1a\u770b\u5230\u7cfb\u7edf\u548c\u50a8\u5e93\u5f62\u6210\u4e86\u4e00\u4e2a\u5fae\u6b63\u5219\u7cfb\u7efc\uff0c\u5176\u4e2d\u80fd\u91cf\u4fdd\u6301\u4e0d\u53d8\uff0c\u6240\u6709\u5fae\u89c2\u72b6\u6001\u7684\u6982\u7387\u5747\u7b49\u3002<\/em><\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5982\u679c\u7cfb\u7edf\u7684\u80fd\u91cf\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">\\varepsilon,<\/span> \u5219\u50a8\u5e93\u7684\u80fd\u91cf\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">E - \\varepsilon.<\/span> \u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7cfb\u7edf\u4e0e\u4e00\u4e2a\u5927\u80fd\u91cf\u50a8\u5e93\u70ed\u63a5\u89e6\uff0c\u79f0\u4e3a<strong>\u6b63\u5219\u7cfb\u7efc\u3002<\/strong><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u73bb\u5c14\u5179\u66fc\u5206\u5e03<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=ch1bjhU7k70&amp;t=528s\" target=\"_blank\" rel=\"noopener\"><strong>\u7cfb\u7edf\u7684\u6982\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">P(\\varepsilon)<\/span><\/strong><\/a>\u5177\u6709\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">\\varepsilon<\/span> \u4e0e\u50a8\u5e93\u53ef\u8bbf\u95ee\u7684\u5fae\u89c2\u72b6\u6001\u6570\u4e58\u4ee5\u7cfb\u7edf\u53ef\u8bbf\u95ee\u7684\u5fae\u89c2\u72b6\u6001\u6570\u6210\u6b63\u6bd4\u3002\u5373\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(\\varepsilon)\\propto \\Omega(E-\\varepsilon)\\cdot 1.<\/span>\n<p>\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u6240\u89c1\uff0c\u6e29\u5ea6\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u8868\u793a\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span> \u7684\u5bf9\u6570\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{1}{k_B T} = \\frac{d\\ln\\Omega}{dE}<\/span>\n<p>\u7531\u4e8e <span class=\"katex-eq\" data-katex-display=\"false\">\\varepsilon \\ll E,<\/span> \u53ef\u4ee5\u5728 <span class=\"katex-eq\" data-katex-display=\"false\">\\varepsilon = 0<\/span> \u9644\u8fd1\u5bf9 <span class=\"katex-eq\" data-katex-display=\"false\">\\ln\\Omega(E-\\varepsilon)<\/span> \u8fdb\u884c\u6cf0\u52d2\u7ea7\u6570\u5c55\u5f00\u3002\u7531\u6b64\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\ln\\Omega(E-\\varepsilon) = \\ln\\Omega(E) - \\frac{d\\ln\\Omega(E)}{dE}\\varepsilon + \\cdots<\/span>\n<p>\u7ed3\u5408\u4ee5\u4e0a\u4e24\u5f0f\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\ln\\Omega(E-\\varepsilon) = \\ln\\Omega(E) - \\frac{\\varepsilon}{k_B T} + \\cdots<\/span>\n<p>\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u662f\u50a8\u5e93\u7684\u6e29\u5ea6\u3002\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u5ffd\u7565\u6cf0\u52d2\u7ea7\u6570\u5c55\u5f00\u7684\u9ad8\u9636\u9879\uff0c\u5e76\u8ba4\u4e3a\u4ee5\u4e0b\u5173\u7cfb\u6210\u7acb\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln \\Omega(E-\\varepsilon) \\approx \\ln\\Omega(E) - \\displaystyle \\frac{\\varepsilon}{k_B T}<\/span>\n<p>\u8fdb\u4e00\u6b65\u5c55\u5f00\u4e0a\u8ff0\u8868\u8fbe\u5f0f\uff0c\u6211\u4eec\u5f97\u51fa\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega(E-\\varepsilon) \\approx \\Omega(E) e^{-\\displaystyle \\frac{\\varepsilon}{k_B T}}<\/span>\n<p>\u73b0\u5728\uff0c\u5c06\u8fd9\u4e00\u7ed3\u679c\u4e0e\u6982\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">P(\\varepsilon)<\/span> \u76f8\u6bd4\u8f83\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u7ed3\u8bba\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(\\varepsilon)\\propto e^{-\\varepsilon\/(k_B T)}<\/span>\n<p>\u7531\u4e8e\u7cfb\u7edf\u4e0e\u50a8\u5e93\u5904\u4e8e\u70ed\u529b\u5b66\u5e73\u8861\uff0c\u5b83\u4eec\u5177\u6709\u76f8\u540c\u7684\u6e29\u5ea6\u3002\u7136\u800c\uff0c\u5c3d\u7ba1\u6e29\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u4fdd\u6301\u6052\u5b9a\uff0c\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">\\varepsilon<\/span> \u5e76\u4e0d\u6052\u5b9a\uff1b\u76f8\u53cd\uff0c\u5b83\u4e0e\u4e00\u4e2a\u6982\u7387\u5206\u5e03\u76f8\u5173\uff0c\u8fd9\u6b63\u662f\u6211\u4eec\u521a\u521a\u63a8\u5bfc\u51fa\u7684\u5206\u5e03\u3002\u8fd9\u88ab\u79f0\u4e3a<strong>\u73bb\u5c14\u5179\u66fc\u5206\u5e03<\/strong>\u6216<strong>\u6b63\u5219\u5206\u5e03<\/strong>\uff0c\u9002\u7528\u4e8e\u6b63\u5219\u7cfb\u7efc\u3002\u9879 <span class=\"katex-eq\" data-katex-display=\"false\">e^{-\\varepsilon\/(k_B T)}<\/span> \u88ab\u79f0\u4e3a<strong>\u73bb\u5c14\u5179\u66fc\u56e0\u5b50\u3002<\/strong><\/p>\n<h3>\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7684\u5f52\u4e00\u5316\u4e0e\u5206\u914d\u51fd\u6570<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=ch1bjhU7k70&amp;t=890s\" target=\"_blank\" rel=\"noopener\"><strong>\u901a\u8fc7\u8fd9\u4e9b\u63a8\u5bfc\uff0c\u6211\u4eec\u5df2\u7ecf\u5f00\u59cb<\/strong><\/a>\u6784\u5efa\u4e00\u4e2a\u6982\u7387\u5206\u5e03\uff0c\u7528\u4e8e\u63cf\u8ff0\u4e00\u4e2a\u5c0f\u7cfb\u7edf\u5728\u4e0e\u6e29\u5ea6\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u7684\u5927\u50a8\u5e93\u8026\u5408\u65f6\u7684\u884c\u4e3a\u3002\u7cfb\u7edf\u6709\u5408\u7406\u7684\u673a\u4f1a\u83b7\u5f97\u4f4e\u4e8e <span class=\"katex-eq\" data-katex-display=\"false\">k_B T<\/span> \u7684\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">\\varepsilon,<\/span> \u4f46\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u4e2d\u7684\u6307\u6570\u9879\u5728\u5c1d\u8bd5\u83b7\u5f97\u66f4\u9ad8\u80fd\u91cf\u65f6\u8fc5\u901f\u8870\u51cf\u3002\u7136\u800c\uff0c\u6211\u4eec\u5fc5\u987b\u6ce8\u610f\u5230\uff0c\u8fd9\u79cd\u5206\u5e03\u76ee\u524d\u5e76\u4e0d\u662f\u4e00\u4e2a\u4e25\u683c\u610f\u4e49\u4e0a\u7684\u6982\u7387\u5206\u5e03\uff1b\u5b83\u9700\u8981\u5f52\u4e00\u5316\u3002\u5982\u679c\u4e00\u4e2a\u7cfb\u7edf\u4e0e\u4e00\u4e2a\u50a8\u5e93\u63a5\u89e6\uff0c\u5e76\u5177\u6709\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">E_r<\/span> \u7684\u5fae\u89c2\u72b6\u6001 <span class=\"katex-eq\" data-katex-display=\"false\">r,<\/span> \u5219\u6211\u4eec\u6709\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P({microstate\\;}r)= \\displaystyle \\frac{e^{-E_r\/(k_B T)}}{\\displaystyle \\sum_{i}e^{-E_i\/(k_B T)}}<\/span>\n<p>\u5206\u6bcd\u4e2d\u7684\u6c42\u548c\u9879\u8d77\u5230\u4e86\u5f52\u4e00\u5316\u56e0\u5b50\u7684\u4f5c\u7528\uff0c\u4f7f <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> \u6210\u4e3a\u4e00\u4e2a\u6982\u7387\u5206\u5e03\u3002\u8fd9\u4e2a\u5206\u6bcd\u7684\u6c42\u548c\u9879\u4e5f\u88ab\u79f0\u4e3a<strong>\u5206\u914d\u51fd\u6570<\/strong>\uff0c\u8bb0\u4f5c <span class=\"katex-eq\" data-katex-display=\"false\">Z<\/span>\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Z = \\displaystyle \\sum_i e^{-E_i\/(k_B T)}<\/span>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/lDtYzvXiNb4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7684\u5e94\u7528<\/h2>\n<p>\u4e3a\u4e86\u8bf4\u660e\u6b63\u5219\u7cfb\u7efc\u548c\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7684\u4e00\u4e9b\u5e94\u7528\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u4e00\u4e9b\u793a\u4f8b\u7814\u7a76\u5b83\u4eec\u7684\u8868\u73b0\u3002\u4e0d\u8fc7\uff0c\u5728\u5f00\u59cb\u4e4b\u524d\uff0c\u6211\u4eec\u5f15\u5165\u4e00\u4e2a\u7ecf\u5e38\u51fa\u73b0\u7684\u91cf\u7684\u7b26\u53f7\uff0c\u5b83\u5728\u672a\u6765\u53ef\u80fd\u4f1a\u5f88\u6709\u7528\u3002\u5b9a\u4e49\u56e0\u5b50 <span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span> \u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta =\\displaystyle  \\frac{1}{k_B T},<\/span>\n<p>\u7531\u6b64\u53ef\u4ee5\u5199\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta = \\displaystyle \\frac{d\\ln\\Omega}{dE},<\/span>\n<h4>\u53ea\u6709\u4e24\u4e2a\u53ef\u80fd\u72b6\u6001\u7684\u7cfb\u7edf\u95ee\u9898<\/h4>\n<p>\u8bbe\u60f3\u6700\u7b80\u5355\u7684\u60c5\u51b5\uff0c\u4e00\u4e2a\u7cfb\u7edf\u53ea\u80fd\u5904\u4e8e\u4e24\u4e2a\u72b6\u6001\uff1a\u4e00\u4e2a\u80fd\u91cf\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span>\uff0c\u53e6\u4e00\u4e2a\u80fd\u91cf\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">\\varepsilon\\gt 0.<\/span> \u7cfb\u7edf\u7684\u5e73\u5747\u80fd\u91cf\u662f\u591a\u5c11\uff1f<\/p>\n<h4>\u7b49\u6e29\u5927\u6c14\u95ee\u9898<\/h4>\n<p>\u7814\u7a76\u5927\u6c14\u7684\u4e00\u79cd\u7b80\u5316\u65b9\u6cd5\u662f\u5047\u8bbe\u5b83\u662f\u7b49\u6e29\u7684\u3002\u5c3d\u7ba1\u8fd9\u4e00\u5047\u8bbe\u5e76\u4e0d\u6210\u7acb\uff0c\u4f46\u4f5c\u4e3a\u7b2c\u4e00\u8fd1\u4f3c\u53ef\u4ee5\u5f97\u51fa\u67d0\u4e9b\u7ed3\u8bba\u3002\u4f8b\u5982\uff1a\u5728\u8fd9\u4e00\u5047\u8bbe\u4e0b\uff0c\u53ef\u4ee5\u4f30\u8ba1\u7ec4\u6210\u5927\u6c14\u7684\u7c92\u5b50\u6570\u91cf\u662f\u9ad8\u5ea6\u7684\u51fd\u6570\u3002\u60a8\u8ba4\u4e3a\u5982\u4f55\u5f97\u51fa\u8fd9\u4e00\u63a8\u8bba\uff1f<\/p>\n<h4>\u7206\u70b8\u5371\u9669\uff01\u5316\u5b66\u53cd\u5e94\u4e0e\u6e29\u5ea6\u4e4b\u95f4\u7684\u5173\u7cfb<\/h4>\n<p>\u8bb8\u591a\u5316\u5b66\u53cd\u5e94\u6709\u4e00\u4e2a\u7279\u5b9a\u7684\u6fc0\u6d3b\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">E_{act}<\/span>\uff0c\u5927\u7ea6\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">1\/2 [eV]<\/span>\u3002\u5728\u6e29\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">T=300[K],<\/span> \u5373\u5ba4\u6e29\u9644\u8fd1\uff0c\u53cd\u5e94\u53d1\u751f\u7684\u6982\u7387\u4e0e\u4ee5\u4e0b\u9879\u6210\u6b63\u6bd4\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">e^{-E_{act}\/(k_B T)}<\/span>\n<p>\u5982\u679c\u6e29\u5ea6\u589e\u52a0 10[K]\uff0c\u53cd\u5e94\u7684\u6982\u7387\u4f1a\u53d1\u751f\u4ec0\u4e48\u53d8\u5316\uff1f<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/Pmthx9bQdO0\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u7ec3\u4e60<\/h2>\n<ol style=\"text-align: justify; color:#000000;\">\n<li>\u4e00\u4e2a\u7cfb\u7edf\u5177\u6709 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u4e2a\u72b6\u6001\uff0c\u8fd9\u4e9b\u72b6\u6001\u53ef\u4ee5\u5177\u6709\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u6216 <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta.<\/span> \u8bc1\u660e\uff0c\u603b\u80fd\u91cf\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">E=r\\Delta<\/span>\uff08\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u662f\u6574\u6570\uff09\u7684\u7cfb\u7edf\u914d\u7f6e\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega(E)<\/span> \u7ed9\u51fa\u4e3a\uff1a\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega(E) =\\displaystyle \\frac{N!}{r!(N-r)!}<\/span>\n<p>\u73b0\u5728\u4ece\u7cfb\u7edf\u4e2d\u79fb\u9664\u4e00\u5c0f\u90e8\u5206\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">s\\Delta,<\/span> \u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">s\\ll r.<\/span> \u8bc1\u660e\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega(E-\\varepsilon) \\approx \\Omega(E)\\displaystyle \\frac{r^s}{(N-r)^s} <\/span>\n<p>\u56e0\u6b64\uff0c\u7cfb\u7edf\u7684\u6e29\u5ea6\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u5173\u7cfb\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{1}{k_B T}  = \\frac{1}{\\Delta}\\ln \\left(\\frac{N-r}{r} \\right) <\/span>\n<p>\u7ed8\u5236 <span class=\"katex-eq\" data-katex-display=\"false\">k_B T<\/span> \u5173\u4e8e <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u7684\u56fe\uff0c\u4ece <span class=\"katex-eq\" data-katex-display=\"false\">r=0<\/span> \u5230 <span class=\"katex-eq\" data-katex-display=\"false\">r=N<\/span>\uff0c\u5e76\u89e3\u91ca\u60a8\u7684\u7ed3\u679c\u3002\n<\/li>\n<p><\/br><\/p>\n<li>\n<p style=\"text-align: justify;\">\u4e00\u4e2a\u80fd\u91cf\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">2[eV]<\/span> \u7684\u53ef\u89c1\u5149\u5149\u5b50\u88ab\u4e00\u4e2a\u4fdd\u6301\u5ba4\u6e29\u7684\u5b8f\u89c2\u7269\u4f53\u5438\u6536\u3002<\/p>\n<p style=\"text-align: justify;\">a) \u5b8f\u89c2\u7269\u4f53\u7684 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span> \u6539\u53d8\u4e86\u591a\u5c11\u500d\uff1f <\/p>\n<p style=\"text-align: justify;\">b) \u8003\u8651\u7531 FM \u9891\u6bb5\u4e2d\u7684\u5929\u7ebf\u53d1\u5c04\u7684\u5149\u5b50\uff08\u5178\u578b\u9891\u7387\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">100[MHz]<\/span>\uff09\u3002\u57fa\u4e8e\u6b64\uff0c\u91cd\u590d\u524d\u4e00\u90e8\u5206\u7684\u8ba1\u7b97\uff0c\u5f53\u5438\u6536\u7684\u5149\u5b50\u6765\u81ea FM \u6e90\u65f6\u3002\u4f7f\u7528\u5173\u7cfb <span class=\"katex-eq\" data-katex-display=\"false\">E=hf<\/span>\uff0c\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u662f\u6ce2\u7684\u9891\u7387\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">h=4,135\\;667\\;696 \\cdot 10^{-15}[eV \\cdot s]<\/span> \u662f\u666e\u6717\u514b\u5e38\u6570\u3002<\/p>\n<\/li>\n<p><\/br><\/p>\n<li>\n<p style=\"text-align: justify;\">\u6c42\u4ee5\u4e0b\u7cfb\u7edf\u7684\u5e73\u5747\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">\\lt{E}\\gt<\/span>\uff1a<\/p>\n<p style=\"text-align: justify;\">a) \u4e00\u4e2a\u5177\u6709 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u4e2a\u72b6\u6001\u7684\u7cfb\u7edf\uff0c\u5176\u4e2d\u6bcf\u4e2a\u72b6\u6001\u53ef\u4ee5\u5177\u6709\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">0, \\varepsilon, 2\\varepsilon, 3\\varepsilon, \\cdots , n\\varepsilon.<\/span>\n<p style=\"text-align: justify;\">b) \u4e00\u4e2a\u8c10\u632f\u5b50\uff0c\u5176\u4e2d\u6bcf\u4e2a\u72b6\u6001\u53ef\u4ee5\u5177\u6709\u80fd\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">0, \\varepsilon, 2\\varepsilon, 3\\varepsilon, \\cdots <\/span>\uff08\u65e0\u4e0a\u9650\uff09\u3002<\/p>\n<\/li>\n<\/ol>\n<p><a href=\"https:\/\/drive.google.com\/file\/d\/1YU3OV7gGxLo-mINPLSMcSc0U7ki3zaqX\/view?usp=sharing\" rel=\"noopener\" target=\"_blank\"><strong>\u5305\u542b\u6240\u6709\u8ba1\u7b97\u7684\u767d\u677f<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u5728\u6b63\u5219\u7cfb\u7efc\u4e2d \u70ed\u529b\u5b66\u63ed\u793a\u4e86\u7269\u7406\u7cfb\u7edf\u5982\u4f55\u8fbe\u5230\u5e73\u8861\uff0c\u4ee5\u53ca\u80fd\u91cf\u548c\u6982\u7387\u5982\u4f55\u51b3\u5b9a\u5176\u884c\u4e3a\u3002\u5728\u672c\u8bfe\u7a0b\u4e2d\uff0c\u6211\u4eec\u5c06\u6df1\u5165\u63a2\u8ba8\u6b63\u5219\u7cfb\u7efc\u548c\u73bb\u5c14\u5179\u66fc\u5206\u5e03\uff0c\u8fd9\u662f\u7406\u89e3\u5316\u5b66\u53cd\u5e94\u548c\u590d\u6742\u7cfb\u7edf\u5e73\u8861\u7684\u57fa\u672c\u5de5\u5177\u3002\u60a8\u5c06\u53d1\u73b0\u8fd9\u4e9b\u601d\u60f3\u5982\u4f55\u5c06\u6e29\u5ea6\u4e0e\u79e9\u5e8f\u548c\u6df7\u4e71\u8054\u7cfb\u8d77\u6765\uff0c\u4ece\u800c\u9884\u6d4b\u770b\u4f3c\u4e0d\u53ef\u9884\u6d4b\u7684\u884c\u4e3a\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5b8c\u6210\u672c\u8bfe\u7a0b\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u8bc6\u522b\u70ed\u529b\u5b66\u7cfb\u7efc\u7684\u7c7b\u578b\uff08\u5fae\u6b63\u5219\u7cfb\u7efc\u3001\u6b63\u5219\u7cfb\u7efc\u548c\u5de8\u6b63\u5219\u7cfb\u7efc\uff09\u3002 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