{"id":59513,"date":"2014-12-24T17:17:18","date_gmt":"2014-12-24T09:17:18","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=59513"},"modified":"2021-10-06T16:12:42","modified_gmt":"2021-10-06T08:12:42","slug":"%e7%a9%bf%e9%9a%a7%ef%bc%88%e9%80%9a%e9%81%8e%e5%8b%a2%e5%a3%98%ef%bc%89tunneling-through-a-potential-barrier","status":"publish","type":"post","link":"http:\/\/localhost\/%e7%a9%bf%e9%9a%a7%ef%bc%88%e9%80%9a%e9%81%8e%e5%8b%a2%e5%a3%98%ef%bc%89tunneling-through-a-potential-barrier\/","title":{"rendered":"\u7a7f\u96a7\uff08\u901a\u904e\u52e2\u58d8\uff09"},"content":{"rendered":"

\u7a7f\u96a7\uff08\u901a\u904e\u52e2\u58d8\uff09Tunneling (through a potential barrier)<\/strong><\/span>
\n\u570b\u7acb\u81fa\u7063\u5927\u5b78\u7269\u7406\u5b78\u7cfb98\u7d1a \u8521\u4ea6\u6db5<\/strong><\/span><\/p>\n

\u5c0f\u6642\u5019\u6211\u5011\u4e5f\u8a31\u90fd\u6709\u4e00\u500b\u7d93\u9a57\uff0c\u9a0e\u8173\u8e0f\u8eca\u770b\u5230\u524d\u65b9\u6709\u4e00\u500b\u5c0f\u659c\u5761\uff0c\u597d\u52dd\u5fc3\u5f37\u7684\u6211\u5011\u6703\u60f3\u8981\u52a0\u8db3\u99ac\u529b\u885d\u4e0a\u53bb\uff0c\u5982\u679c\u659c\u5761\u4e0d\u9ad8\u7684\u8a71\uff0c\u8f15\u800c\u4e00\u8209\u5c31\u904e\u53bb\u4e86\uff0c\u8981\u662f\u659c\u5761\u5f88\u9ad8\uff0c\u6211\u5011\u5728\u534a\u8def\u5c31\u505c\u4e0b\u4f86\u4e86\u3002<\/p>\n

\u5728\u53e4\u5178\u529b\u5b78\u88e1\u9762\uff0c\u82e5\u4e00\u500b\u7269\u9ad4\u7684\u7e3d\u80fd\u91cf\u6bd4\u524d\u65b9\u969c\u7919\u7684\u4f4d\u80fd\u9084\u8981\u5c0f\u7684\u8a71\uff0c\u5247\u8a72\u7269\u9ad4\u7121\u6cd5\u514b\u670d\u4f4d\u80fd\u969c\u7919\u53bb\u5230\u9054\u53e6\u4e00\u7aef(\u57161)\u3002<\/p>\n

\"Fig<\/a>

\u57161 (\u9673\u7fa9\u88d5\u7e6a)<\/p><\/div>\n

\u4f46\u662f\u5728\u91cf\u5b50\u529b\u5b78\u7684\u4e16\u754c\u88e1\u537b\u4e0d\u4e00\u5b9a\u662f\u5982\u6b64\u3002\u82e5\u7269\u9ad4\u7684\u5c3a\u5ea6\u5c0f\u5230\u91cf\u5b50\u6548\u61c9\u660e\u986f\u7684\u8a71\uff0c\u5373\u4f7f\u7e3d\u80fd\u91cf\u6bd4\u4f4d\u80fd\u9084\u4f4e\uff0c\u53ea\u8981\u4f4d\u80fd\u4e0d\u662f\u7121\u9650\u5927\uff0c\u4e5f\u4e0d\u662f\u7121\u7aae\u5bec\uff0c\u7684\u78ba\u662f\u6709\u6a5f\u6703\u7a7f\u900f\u904e\u53bb\uff0c\u6211\u5011\u5c07\u5b83\u7a31\u70ba\u7a7f\u96a7\u6548\u61c9(tunneling effect)\u3002<\/p>\n

\u9019\u807d\u8d77\u4f86\u5f88\u4e0d\u53ef\u601d\u8b70\uff0c\u5f88\u50cf\u662f\u79d1\u5e7b\u5c0f\u8aaa\u6216\u662f\u79d1\u5e7b\u96fb\u5f71\u624d\u6703\u51fa\u73fe\u7684\u60c5\u7bc0\uff0c\u800c\u9019\u4e5f\u5c31\u662f\u91cf\u5b50\u529b\u5b78\u4ee4\u4eba\u96e3\u4ee5\u6349\u6478\u4e14\u8ff7\u4eba\u7684\u5730\u65b9\u3002\u4e4b\u6240\u4ee5\u6703\u6709\u4e0a\u8ff0\u7684\u60c5\u7bc0\u8207\u53ef\u80fd\u6027\uff0c\u6700\u91cd\u8981\u7684\u539f\u56e0\u4fbf\u662f\uff1a\u7269\u8cea\u7c92\u5b50\u5728\u7a7a\u9593\u4e2d\u7684\u5206\u5e03\u662f\u6a5f\u7387\u6027\u7684\uff0c\u800c\u6b64\u6a5f\u7387\u5206\u5e03\u53c8\u5177\u6709\u6ce2\u52d5\u7684\u7279\u6027\u3002<\/p>\n

\u6839\u64da\u5fb7\u5e03\u7f85\u610f<\/a>(de Broglie)\u63d0\u51fa\u7269\u8cea\u6ce2(matter wave)\u7684\u6982\u5ff5\uff0c\u8a8d\u70ba\u7269\u8cea\u540c\u6642\u5177\u6709\u7c92\u5b50\u8207\u6ce2\u52d5\u7684\u7279\u6027\uff0c\u800c\u7269\u8cea\u6ce2\u7684\u6ce2\u9577 $$\\lambda$$ \u6eff\u8db3\u7b49\u5f0f\uff1a<\/p>\n

$$\\lambda=\\displaystyle\\frac{h}{p}$$<\/p>\n

\u5176\u4e2d $$h$$ \u70ba\u666e\u6717\u514b\u5e38\u6578\uff0c$$p$$ \u70ba\u52d5\u91cf\u3002\u6b64\u5916\uff0c\u7528\u4f86\u8a08\u7b97\u7269\u8cea\u6ce2\u5728\u7a7a\u9593\u4e2d\u51fa\u73fe\u6a5f\u7387\u7684\u6240\u8b02\u6ce2\u51fd\u6578 $$\\Psi(x)$$ \u5247\u53ef\u7531\u4ee5\u4e0b\u7684\u6ce2\u65b9\u7a0b\u5f0f\u4f86\u63cf\u8ff0\uff1a<\/p>\n

$$\\displaystyle -\\frac{\\hbar^2}{2m}\\frac{\\mathrm{d}^2}{\\mathrm{d}x^2}\\Psi(x)+V(x)\\Psi(x)=E\\Psi(x)$$<\/p>\n

\u9019\u662f\u4e00\u7dad\u7684\u975e\u542b\u6642\u859b\u4e01\u683c\u65b9\u7a0b\u5f0f(time-independent Schr\u00f6dinger equation)\uff0c $$\\hbar$$\u00a0\u70ba\u5316\u7d04\u666e\u6717\u514b\u5e38\u6578\uff0c$$E$$ \u662f\u7cfb\u7d71\u7e3d\u80fd\u91cf\u3002\u53ea\u8981\u4f4d\u80fd\u975e\u7121\u7aae\u5927\uff0c\u5c31\u4e00\u5b9a\u53ef\u4ee5\u89e3\u51fa\u6ce2\u51fd\u6578\u7684\u89e3\u3002\u5373\u4f7f\u7e3d\u80fd\u91cf\u5c0f\u65bc\u4f4d\u80fd\uff0c\u4e5f\u6703\u6709\u6ce2\u51fd\u6578\u5b58\u5728\uff0c\u65bc\u662f\u7c92\u5b50\u5c31\u4ecd\u6709\u5728\u8a72\u5340\u57df\u4e2d\u51fa\u73fe\u7684\u6a5f\u6703\u3002<\/p>\n

\u6211\u5011\u4e5f\u53ef\u4ee5\u7528\u4ee5\u4e0b\u66f4\u76f4\u89c0\u7684\u65b9\u5f0f\u53bb\u89e3\u91cb\u7a7f\u96a7\u6548\u61c9\u3002\u5148\u89c0\u5bdf\u57162\u7684\u96fb\u8166\u6a21\u64ec\u52d5\u756b\u3002<\/p>\n

\"Fig<\/a>

\u57162 (\u9673\u7fa9\u88d5\u7e6a)<\/p><\/div>\n

\u5047\u8a2d\u6709\u4e00\u500b\u7c92\u5b50\u81ea\u5de6\u908a\u5165\u5c04\uff0c\u5b83\u7684\u80fd\u91cf(\u85cd\u8272\u76f4\u7dda\u9ad8\u5ea6)\u6bd4\u7d05\u8272\u969c\u7919\u7684\u6700\u9ad8\u9ede\u4e4b\u80fd\u91cf\u7a0d\u4f4e\uff0c\u5247\u6b64\u7c92\u5b50\u5728\u53e4\u5178\u7269\u7406\u4e2d\u662f\u7121\u6cd5\u8d85\u8d8a\u7d05\u8272\u969c\u7919\u800c\u8dd1\u5230\u53f3\u5074\u7684\u3002\u4f46\u8a72\u7c92\u5b50\u9075\u5b88\u7684\u662f\u91cf\u5b50\u529b\u5b78\uff0c\u5176\u6240\u5c0d\u61c9\u7684\u7269\u8cea\u6ce2(\u7da0\u8272)\u65bc\u9032\u5165\u5230\u7d05\u8272\u969c\u7919\u5340\u7684\u5de6\u5074\u6642\uff0c\u4e00\u5b9a\u6709\u90e8\u5206\u7a7f\u900f\u3001\u90e8\u5206\u53cd\u5c04\uff0c\u7a7f\u900f\u90e8\u5206\u63a5\u8457\u5c31\u5728\u4f4d\u80fd\u8f03\u9ad8\u7684\u5730\u65b9\u9032\u884c\u50b3\u905e\uff0c\u76f4\u5230\u7576\u5b83\u649e\u5230\u4e86\u7d05\u8272\u969c\u7919\u7684\u53f3\u908a\u754c\uff0c\u6b64\u6642\u53c8\u6703\u6709\u90e8\u5206\u7a7f\u900f\u3001\u90e8\u5206\u53cd\u5c04\uff0c\u800c\u7a7f\u900f\u7684\u90e8\u5206\u6b64\u5f8c\u4fbf\u53ef\u7e7c\u7e8c\u671d\u53f3\u65b9\u50b3\u64ad\uff0c\u9019\u5c31\u662f\u7a7f\u96a7\u3002<\/p>\n

\u4e0a\u9762\u7684\u5716\u50cf\u96d6\u89e3\u91cb\u4e86\u7a7f\u96a7\u767c\u751f\u7684\u53ef\u80fd\uff0c\u4f46\u6ce2\u5728\u4f4d\u80fd\u8f03\u9ad8\u7684\u5730\u65b9\u5f80\u53f3\u50b3\u905e\u7562\u7adf\u662f\u5341\u5206\u8f9b\u82e6\u7684\uff0c\u6bcf\u591a\u8d70\u4e00\u6b65\uff0c\u5b83\u80fd\u51fa\u73fe\u5728\u53f3\u65b9\u7684\u6a5f\u7387\u5c31\u964d\u4f4e\u8a31\u591a\uff0c\u8981\u662f\u969c\u7919\u5340\u57df\u904e\u5bec\uff0c\u7a7f\u900f\u7684\u6bd4\u4f8b\u592a\u4f4e\uff0c\u7a7f\u96a7\u6548\u61c9\u53ef\u80fd\u5c31\u4e0d\u90a3\u9ebc\u986f\u8457\u4e86\uff1b\u9664\u6b64\u4e4b\u5916\uff0c\u4f4d\u80fd\u969c\u7919\u8d8a\u9ad8\uff0c\u8981\u7a7f\u900f\u7684\u6a5f\u6703\u4e5f\u6703\u8d8a\u5c0f\u3002<\/p>\n

\u7e3d\u800c\u8a00\u4e4b\uff0c\u7406\u8ad6\u4e0a\u53ea\u8981\u4f4d\u80fd\u969c\u7919\u4e0d\u662f\u7121\u9650\u5927\u3001\u5bec\u5ea6\u4e0d\u662f\u7121\u7aae\u5bec\uff0c\u90fd\u6703\u6709\u7a7f\u96a7\u7684\u73fe\u8c61\uff0c\u7d93\u904e\u8a08\u7b97\uff0c\u7a7f\u96a7\u7684\u6bd4\u4f8b\u6eff\u8db3\uff1a<\/p>\n

$$T=e^{\\displaystyle-\\frac{2}{\\hbar}\\int^a_0\\sqrt{2m(V(x)-E)}\\mathrm{d}x}$$<\/p>\n

\u5176\u4e2d $$a$$ \u662f\u4f4d\u80fd\u969c\u7919\u7684\u5bec\u5ea6\u3002\u7531\u9019\u516c\u5f0f\u4e2d\u4e5f\u53ef\u4ee5\u6e05\u695a\u770b\u5230\uff0c$$V(x)$$ \u8d8a\u5927\uff0c\u6216\u8005 $$a$$ \u8d8a\u5927\uff0c$$T$$ \u90fd\u6703\u8b8a\u5c0f\uff0c\u6eff\u8db3\u4e0a\u8ff0\u7684\u8a0e\u8ad6\u3002\u4f46\u662f\u516c\u5f0f\u4e2d\u4e5f\u53ef\u4ee5\u6e05\u695a\u770b\u5230\uff0c\u6709\u4e00\u500b\u6578\u503c\u975e\u5e38\u5c0f\u7684 $$\\hbar$$\u00a0\u5728\u90a3\u88cf\uff0c\u6545\u5c0d\u5de8\u89c0\u7684\u7cfb\u7d71\u4f86\u8aaa\uff0c\u7a7f\u96a7\u7684\u6a5f\u7387\u90fd\u8da8\u8fd1\u65bc\u96f6\uff0c\u6240\u4ee5\u6211\u5011\u5e73\u5e38\u5e7e\u4e4e\u770b\u4e0d\u5230\u7a7f\u96a7\u73fe\u8c61\uff0c\u4f46\u5982\u679c\u6211\u5011\u628a $$a$$ \u4e5f\u5f04\u5f97\u5f88\u5c0f\uff0c$$V(x)$$ \u4e0d\u8981\u592a\u5927\uff0c\u9019\u6a23\u7a7f\u96a7\u6548\u61c9\u5c31\u8d8a\u4f86\u8d8a\u986f\u8457\u3002<\/p>\n

\u91cf\u5b50\u529b\u5b78\u7684\u6839\u672c\u5047\u8a2d\u5e7e\u4e4e\u5c31\u9020\u5c31\u7a7f\u96a7\u6548\u61c9\u7684\u5fc5\u7136\uff0c\u7a7f\u96a7\u6548\u61c9\u88ab\u767c\u73fe\u4e4b\u5f8c\uff0c\u5c0d\u65bc\u79d1\u6280\u61c9\u7528\u7522\u751f\u5f88\u591a\u65b0\u7684\u60f3\u6cd5\uff0c\u5176\u4e2d\u6383\u63cf\u7a7f\u96a7\u986f\u5fae\u93e1(scanning tunneling microscope, STM)\u5c31\u662f\u4e00\u500b\u4f8b\u5b50\uff0c\u9019\u500b\u986f\u5fae\u93e1\u7684\u767c\u660e\u8b93\u6211\u5011\u80fd\u5c0d\u65bc\u5fae\u89c0\u7684\u5c3a\u5ea6\u505a\u66f4\u6df1\u5165\u7684\u63a2\u7a76\u3002<\/p>\n

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

    \n
  1. \u7dad\u57fa\u767e\u79d1. Quantum tunneling. http:\/\/en.wikipedia.org\/wiki\/Quantum_tunnelling<\/a><\/li>\n
  2. Griffiths, D. J. (2004). Introduction to quantum mechanics(Chapter 8. WKB approximation), 2nd edition. Pearson Prentice Hall.<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u7a7f\u96a7\uff08\u901a\u904e\u52e2\u58d8\uff09Tunneling (through a potential barrier) \u570b\u7acb\u81fa\u7063\u5927\u5b78\u7269…<\/p>\n","protected":false},"author":50,"featured_media":60720,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107,32,35],"tags":[1323,2767,1071],"class_list":["post-59513","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-physics00","category-physics07","category-physics07-03","tag-1323","tag-2767","tag-1071","loop-entry","cat-107","cat-32","cat-35"],"views":29306,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/59513","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=59513"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/59513\/revisions"}],"predecessor-version":[{"id":86696,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/59513\/revisions\/86696"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media\/60720"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=59513"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=59513"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=59513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}