{"id":46520,"date":"2026-06-23T17:00:30","date_gmt":"2026-06-23T09:00:30","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=46520"},"modified":"2026-06-23T14:03:20","modified_gmt":"2026-06-23T06:03:20","slug":"%e5%8e%9f%e5%ad%90%e5%bd%88%e7%88%86%e7%82%b8%e4%b9%8b%e5%89%8d%ef%bc%8c%e5%a5%a7%e6%9c%ac%e6%b5%b7%e9%bb%98%e6%8b%86%e8%a7%a3%e4%ba%86%e9%87%8f%e5%ad%90%e7%9a%84%e4%b8%96%e7%95%8c","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=46520","title":{"rendered":"\u539f\u5b50\u5f48\u7206\u70b8\u4e4b\u524d\uff0c\u5967\u672c\u6d77\u9ed8\u62c6\u89e3\u4e86\u91cf\u5b50\u7684\u4e16\u754c"},"content":{"rendered":"

\u5728\u539f\u5b50\u5f48\u7206\u70b8\u4e4b\u524d\uff0c\u5e74\u8f15\u7684\u5967\u672c\u6d77\u9ed8\u65e9\u5df2\u6539\u8b8a\u4e86\u4e16\u754c\u3002\u7576\u4eba\u985e\u7b2c\u4e00\u6b21\u8a66\u5716\u9810\u6e2c\u5fae\u89c0\u4e16\u754c\u7684\u7c92\u5b50\u4f5c\u7528\u6642\uff0c\u79d1\u5b78\u5bb6\u767c\u73fe\uff0c\u96fb\u5b50\u8207\u539f\u5b50\u6838\u7684\u4ea4\u4e92\u4f5c\u7528\u8907\u96dc\u5230\u5e7e\u4e4e\u7121\u6cd5\u8a08\u7b97\uff0c\u7136\u800c\uff0c\u5967\u672c\u6d77\u9ed8\u8207\u73bb\u6069\u63d0\u51fa\u4e86\u4e00\u500b\u60f3\u6cd5\uff1a\u300c\u96fb\u5b50\u5f88\u5feb\uff0c\u539f\u5b50\u6838\u5f88\u6162\uff0c\u56e0\u6b64\u5b83\u5011\u53ef\u4ee5\u88ab\u62c6\u958b\u8655\u7406\u3002\u300d\u9019\u500b\u88ab\u7a31\u70ba\u300c\u73bb\u6069\u2013\u5967\u672c\u6d77\u9ed8\u8fd1\u4f3c\u300d\u7684\u7406\u8ad6\uff0c\u4e0d\u53ea\u8b93\u91cf\u5b50\u4e16\u754c\u958b\u59cb\u8b8a\u5f97\u53ef\u8a08\u7b97\uff0c\u66f4\u6210\u70ba\u4eca\u65e5\u6750\u6599\u79d1\u5b78\u3001\u534a\u5c0e\u9ad4\u6a21\u64ec\u3001\u85e5\u7269\u8a2d\u8a08\u8207\u4eba\u5de5\u667a\u6167\u6750\u6599\u958b\u767c\u7684\u57fa\u790e\u3002\u539f\u4f86\uff0c\u5728\u6210\u70ba\u539f\u5b50\u5f48\u4e4b\u7236\u4e4b\u524d\uff0c\u5967\u672c\u6d77\u9ed8\u65e9\u5df2\u6084\u6084\u62c6\u89e3\u4e86\u91cf\u5b50\u7684\u4e16\u754c\u3002<\/strong><\/span><\/p>\n

\u64b0\u6587\uff5c\u9ec3\u9f0e\u921e<\/strong><\/p>\n

\u63d0\u5230\u5967\u672c\u6d77\u9ed8 (Julius Robert Oppenheimer, 1904\u20131967)\uff0c\u8a31\u591a\u4eba\u7b2c\u4e00\u500b\u60f3\u5230\u7684\uff0c\u662f\u6c99\u6f20\u3001\u5012\u6578\u3001\u9583\u5149\uff0c\u4ee5\u53ca\u90a3\u53e5\u4ee4\u4eba\u6230\u6144\u7684\u8a71\uff1a\u300c\u6211\u6210\u4e86\u6b7b\u795e\uff0c\u4e16\u754c\u7684\u6bc0\u6ec5\u8005\u3002\u300d\u5728\u96fb\u5f71\u7684\u63a8\u6ce2\u52a9\u703e\u4e0b\uff0c\u518d\u6b21\u6210\u70ba\u5927\u773e\u719f\u6089\u7684\u540d\u5b57\u3002\u4ed6\u662f\u66fc\u54c8\u9813\u8a08\u756b\u7684\u6838\u5fc3\u4eba\u7269\uff0c\u662f\u539f\u5b50\u5f48\u4e4b\u7236\u3002<\/p>\n

\u82e5\u6211\u5011\u53ea\u8a18\u5f97\u5967\u672c\u6d77\u9ed8\u662f\u539f\u5b50\u5f48\u4e4b\u7236\uff0c\u90a3\u5c31\u53ea\u770b\u898b\u4e86\u4ed6\u4e00\u751f\u4e2d\u6700\u6c89\u91cd\u7684\u4e00\u9762\u3002<\/p>\n

\u5728\u5967\u672c\u6d77\u9ed8\u6210\u70ba\u6d1b\u65af\u963f\u62c9\u83ab\u65af\u5be6\u9a57\u5ba4\u7684\u9818\u5c0e\u8005\u4ee5\u524d\uff0c\u4ed6\u65e9\u5df2\u662f\u4e00\u4f4d\u5091\u51fa\u7684\u7406\u8ad6\u7269\u7406\u5b78\u5bb6\uff0c\u4ed6\u4e0d\u53ea\u53c3\u8207\u6838\u7269\u7406\uff0c\u4e5f\u6d89\u8db3\u91cf\u5b50\u529b\u5b78\u3001\u5206\u5b50\u7269\u7406\u3001\u5b87\u5b99\u7dda\u3001\u76f8\u5c0d\u8ad6\u8207\u5f8c\u4f86\u88ab\u8996\u70ba\u9ed1\u6d1e\u524d\u8eab\u7684\u91cd\u529b\u574d\u7e2e\u7814\u7a76\u3002\u5728\u4ed6\u7684\u65e9\u671f\u79d1\u5b78\u751f\u6daf\u4e2d\uff0c\u6709\u4e00\u500b\u4ee5\u4ed6\u8207\u73bb\u6069 (Max Born, 1882\u20131970) \u5171\u540c\u547d\u540d\u7684\u7406\u8ad6\u8fd1\u4f3c\uff0c\u76f4\u5230\u4eca\u5929\u4ecd\u6bcf\u5929\u51fa\u73fe\u5728\u6750\u6599\u79d1\u5b78\u3001\u534a\u5c0e\u9ad4\u7269\u7406\u8207\u5206\u5b50\u6a21\u64ec\u4e4b\u4e2d\uff0c\u4e5f\u5c31\u662f\u300c\u73bb\u6069\u2013\u5967\u672c\u6d77\u9ed8\u8fd1\u4f3c (Born\u2013Oppenheimer approximation)\u300d\u3002<\/p>\n

\u5b83\u6c92\u6709\u7206\u70b8\u8072\uff0c\u6c92\u6709\u8611\u83c7\u96f2\uff0c\u4e5f\u6c92\u6709\u653f\u6cbb\u8272\u5f69\uff0c\u4e0d\u50cf\u539f\u5b50\u5f48\u90a3\u6a23\u9707\u64bc\u4e16\u754c\uff0c\u4e5f\u9bae\u5c11\u51fa\u73fe\u5728\u6b77\u53f2\u8ab2\u672c\u7684\u5de8\u5927\u6a19\u984c\u88e1\uff0c\u7136\u800c\uff0c\u5b83\u537b\u652f\u6490\u8d77\u73fe\u4ee3\u79d1\u5b78\u4e2d\u4e00\u5927\u7247\u8a08\u7b97\u4e16\u754c\uff0c\u4eca\u5929\u6211\u5011\u7528\u96fb\u8166\u6a21\u64ec\u5206\u5b50\u3001\u8a08\u7b97\u6750\u6599\u80fd\u5e36\u3001\u9810\u6e2c\u5316\u5b78\u53cd\u61c9\u3001\u7406\u89e3\u534a\u5c0e\u9ad4\u3001\u7814\u7a76\u85e5\u7269\uff0c\u90fd\u76f4\u63a5\u6216\u9593\u63a5\u7ad9\u5728\u9019\u4e00\u500b\u7b97\u5f0f\u7684\u57fa\u790e\u4e4b\u4e0a\u3002<\/p>\n

\u56e0\u70ba\uff0c\u5b83\u628a\u4e00\u500b\u5e7e\u4e4e\u7121\u6cd5\u8655\u7406\u7684\u5b87\u5b99\u7d1a\u96e3\u984c\uff0c\u8b8a\u6210\u4e86\u4e00\u500b\u4eba\u985e\u53ef\u4ee5\u8655\u7406\u7684\u554f\u984c\u3002<\/p>\n

\"\"
\u57161\uff1a\u5967\u672c\u6d77\u9ed8 (Julius Robert Oppenheimer, 1904-1967)\uff5c\u4f86\u6e90\uff1aWikimedia Commons<\/figcaption><\/figure>\n

 <\/p>\n

\u91cf\u5b50\u529b\u5b78\u525b\u8a95\u751f\u6642\uff0c\u4e16\u754c\u8b8a\u5f97\u592a\u8907\u96dc\u4e86<\/strong><\/span><\/h6>\n

\u4e8c\u5341\u4e16\u7d00\u521d\uff0c\u4eba\u5011\u76f8\u4fe1\u53ea\u8981\u77e5\u9053\u7c92\u5b50\u7684\u4f4d\u7f6e\u548c\u901f\u5ea6\uff0c\u6839\u64da\u725b\u9813 (Isaac Newton, 1643\u20131727) \u529b\u5b78\u5c31\u80fd\u9810\u6e2c\u672a\u4f86\u3002\u4f46\u662f\u96a8\u8457\u79d1\u5b78\u5bb6\u5c0d\u5fae\u89c0\u4e16\u754c\u7684\u4e86\u89e3\uff0c\u9019\u5957\u529b\u5b78\u67b6\u69cb\u958b\u59cb\u9b06\u52d5\uff0c\u56e0\u70ba\u96fb\u5b50\u4e0d\u662f\u7e5e\u8457\u539f\u5b50\u6838\u65cb\u8f49\u7684\u5c0f\u884c\u661f\uff0c\u539f\u5b50\u4e5f\u4e0d\u662f\u5fae\u7e2e\u7248\u7684\u592a\u967d\u7cfb\uff0c\u5728\u9019\u5fae\u89c0\u7684\u4e16\u754c\u88e1\uff0c\u7c92\u5b50\u5177\u6709\u6ce2\u7684\u6027\u8cea\uff0c\u4f4d\u7f6e\u53ea\u80fd\u7528\u6a5f\u7387\u4f86\u63cf\u8ff0\u3002<\/p>\n

\u76f4\u5230\u859b\u4e01\u683c\uff08Erwin Schr\u00f6dinger, 1887\u20131961\uff09\u65b9\u7a0b\u5f0f\u7684\u51fa\u73fe\uff0c\u79d1\u5b78\u5bb6\u624d\u958b\u59cb\u6709\u63cf\u8ff0\u5fae\u89c0\u4e16\u754c\u7684\u6578\u5b78\u6a21\u578b\uff0c\u900f\u904e\u6c42\u89e3\u6ce2\u51fd\u6578\uff0c\u624d\u80fd\u77e5\u9053\u96fb\u5b50\u5728\u539f\u5b50\u3001\u5206\u5b50\u6216\u6750\u6599\u4e2d\u7684\u884c\u70ba\u3002\u6ce2\u51fd\u6578\u53ef\u4ee5\u5beb\u6210\uff1a\u03a8 <\/em>(r , R<\/em>)\uff0c\u5176\u4e2dr\u4ee3\u8868\u96fb\u5b50\u7684\u4f4d\u7f6e\uff0cR\u4ee3\u8868\u539f\u5b50\u6838\u7684\u4f4d\u7f6e\u3002<\/p>\n

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 <\/p>\n

\u96fb\u5b50\u5f88\u5feb\uff0c\u539f\u5b50\u6838\u5f88\u6162<\/strong><\/span><\/h6>\n

\u73bb\u6069\u2013\u5967\u672c\u6d77\u9ed8\u8fd1\u4f3c\u7684\u6838\u5fc3\u6982\u5ff5\uff1a\u300c\u96fb\u5b50\u5f88\u8f15\uff0c\u539f\u5b50\u6838\u5f88\u91cd\uff0c\u5b83\u5011\u7684\u904b\u52d5\u901f\u5ea6\u5dee\u5f88\u591a\uff0c\u6240\u4ee5\u53ef\u4ee5\u5206\u958b\u8655\u7406\u3002\u300d<\/p>\n

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\u56e0\u6b64\uff0c\u7e3d\u6ce2\u51fd\u6578\u53ef\u4ee5\u88ab\u6539\u5beb\u6210\uff1a\u03a8<\/em>(r , R<\/em>)\u2248\u03a8e<\/sub> <\/em>(r <\/em>; R<\/em>) \u03c7N<\/sub><\/em> (R)<\/p>\n

\u03a8e<\/sub> <\/em>(r ; R<\/em>) \u662f\u96fb\u5b50\u6ce2\u51fd\u6578\uff0c\u4e5f\u5c31\u662f\u5728\u67d0\u4e00\u7d44\u56fa\u5b9a\u7684\u539f\u5b50\u6838\u4f4d\u7f6eR\u4e0b\uff0c\u96fb\u5b50\u5982\u4f55\u5206\u5e03\uff0c\u800c\u03c7N<\/sub><\/em> (R) \u5247\u63cf\u8ff0\u539f\u5b50\u6838\u7684\u904b\u52d5\uff0c\u5f0f\u5b50\u88e1\u7684\u5206\u865f\uff1b\u6307\u7684\u662f\u96fb\u5b50\u51fd\u6578\u5148\u5728\u300c\u7d66\u5b9a\u539f\u5b50\u6838\u4f4d\u7f6e\u300d\u7684\u689d\u4ef6\u4e0b\u88ab\u6c42\u89e3\u3002<\/p>\n

 <\/p>\n

\u5f9e\u4e00\u500b\u8fd1\u4f3c\uff0c\u5230\u6574\u500b\u5206\u5b50\u4e16\u754c\u7684\u5730\u5716<\/strong><\/span><\/h6>\n

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\"\"
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\"\"
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 <\/p>\n

\n

\u53c3\u8003\u6587\u737b<\/strong><\/p>\n

    \n
  1. Combes, J. M. (1977, January). The born-oppenheimer approximation. In The Schr\u00f6dinger Equation: Proceedings of the International Symposium \u201c50 Years Schr\u00f6dinger Equation\u201d in Vienna, 10th\u201312th June 1976 (pp. 139-159). Vienna: Springer Vienna.<\/li>\n
  2. Ess\u00e9n, H. (1977). The physics of the Born\u2013Oppenheimer approximation. International Journal of Quantum Chemistry, 12(4), 721-735.<\/li>\n
  3. Tuckerman, M. E., Ungar, P. J., Von Rosenvinge, T., & Klein, M. L. (1996). Ab initio molecular dynamics simulations. The Journal of Physical Chemistry, 100(31), 12878-12887.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

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