{"id":1323,"date":"2022-06-30T22:29:21","date_gmt":"2022-06-30T14:29:21","guid":{"rendered":"http:\/\/www.7mgh.com\/?p=1323"},"modified":"2023-03-22T18:44:41","modified_gmt":"2023-03-22T10:44:41","slug":"%e6%9c%80%e5%b0%8f%e5%b0%ba%e5%ba%a6%e6%99%ae%e6%9c%97%e5%85%8b%e9%95%bf%e5%ba%a6","status":"publish","type":"post","link":"https:\/\/www.7mgh.com\/?p=1323","title":{"rendered":"\u666e\u6717\u514b\u957f\u5ea6\u7684\u63a8\u5bfc"},"content":{"rendered":"\n

\u4eba\u7c7b\u53ea\u80fd\u628a\u7a7a\u95f4\u6700\u5c0f\u5c3a\u5ea6\u7814\u7a76\u5230$1.616229\u00d710^{-35}m$\uff0c\u8fd9\u5e76\u975e\u6280\u672f\u7684\u9650\u5236\uff0c\u800c\u662f\u81ea\u7136\u89c4\u5f8b\uff0c\u4f4e\u4e8e\u8fd9\u4e2a\u5c3a\u5ea6\u7814\u7a76\u7269\u7406\u5c06\u4f1a\u53d8\u5f97\u6ca1\u6709\u610f\u4e49\u3002\u5c31\u597d\u6bd4\u5bf9\u4e8e\u4e00\u5757\u663e\u793a\u5668\uff0c\u6700\u5c0f\u5c3a\u5ea6\u5c31\u662f\u4e00\u4e2a\u50cf\u7d20\uff0c\u6570\u5b66\u4e0a\u5f53\u7136\u53ef\u4ee5\u7ee7\u7eed\u5f80\u4e0b\u5206\uff0c\u7136\u800c\u5bf9\u4e8e\u6210\u50cf\u5df2\u7ecf\u6ca1\u6709\u610f\u4e49\u3002<\/p>\n\n\n\n

\u8fd9\u4e2a\u5c3a\u5ea6\u600e\u4e48\u63a8\u5bfc\u7684\u5462\uff1f<\/p>\n\n\n\n

\u6d4b\u91cf\u80af\u5b9a\u9700\u8981\u5c3a\u5b50\uff0c\u7cbe\u5ea6\u8d8a\u9ad8\uff0c\u6d4b\u91cf\u8d8a\u51c6\uff0c\u5982\u679c\u662f\u6d4b\u91cf\u7535\u5b50\uff0c\u751a\u81f3\u66f4\u5c0f\u7684\u7c92\u5b50\uff0c\u4e0d\u7ba1\u591a\u4e48\u7cbe\u5bc6\u7684\u5c3a\u5b50\u90fd\u5931\u53bb\u610f\u4e49\uff0c\u5373\u4fbf\u4f60\u6709\u4e00\u4e2a\u975e\u5e38\u5c0f\u7684\u5c3a\u5b50\uff0c\u53c8\u5982\u4f55\u56fa\u5b9a\u7c92\u5b50\u5462\uff1f<\/p>\n\n\n\n

\u7531\u4e8e\u5149\u662f\u6ca1\u6709\u9759\u8d28\u91cf\u7684\uff0c\u4e8e\u662f\u79d1\u5b66\u5bb6\u5e72\u8106\u7528\u5149\u6765\u6d4b\u91cf\uff0c\u800c\u4e14\u76f8\u5bf9\u8bba\u4f53\u7cfb\u4e0b\uff0c\u5149\u901f\u662f\u6052\u5b9a\u7684\uff0c\u6240\u4ee5\u7528\u5149\u6765\u6d4b\u91cf\u662f\u6700\u4f18\u65b9\u6848\uff0c\u8981\u63d0\u6d4b\u91cf\u7684\u7cbe\u5ea6\uff0c\u5c31\u8981\u4e0d\u65ad\u7684\u51cf\u5c0f\u6ce2\u957f\uff0c\u90a3\u4e48\u6d4b\u91cf\u7684\u7cbe\u5ea6\u81ea\u7136\u4f1a\u8d8a\u9ad8\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u7528\u5149\u6d4b\u8ddd\u662f\u597d\u7684\u529e\u6cd5\uff0c\u5e7f\u6cdb\u4f7f\u7528\u7684\u6fc0\u5149\u6d4b\u8ddd\u4eea\u5df2\u7ecf\u8bf4\u660e\u4e86\u8fd9\u4e00\u70b9\uff0c\u4f46\u5fae\u89c2\u4e16\u754c\uff0c\u7528\u5149\u6d4b\u91cf\u5c31\u4f1a\u9047\u5230\u9ebb\u70e6\u3002<\/p>\n\n\n\n

$$E = \\hbar \\nu $$<\/p>\n\n\n\n

\u7531\u4e8e$c = \\lambda \\nu $\uff0c\u63d0\u9ad8\u7cbe\u5ea6\u5c31\u8981\u63d0\u9ad8\u9891\u7387$\\nu $\uff0c\u63d0\u9ad8$\\nu $\u5149\u5b50\u7684\u80fd\u91cf\u5c31\u4f1a\u53d8\u5927\uff0c\u90a3\u5fae\u89c2\u7c92\u5b50\u5c31\u4f1a\u88ab\u649e\u98de\u3002<\/p>\n\n\n\n

\"\"\/
\u6ce2\u957f\u4e0e\u52a8\u91cf\u5173\u7cfb\u5f0f\uff0c\u6d4b\u91cf\u5c3a\u5ea6\u6781\u9650\u5c31\u662f\u6700\u5c0f\u6ce2\u957f\u3002<\/figcaption><\/figure>\n\n\n\n

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

\u5728\u5fae\u89c2\u5c3a\u5ea6\u6ce2\u957f\u7b49\u4ef7\u4e8e\u8ddd\u79bb\uff0c$\\lambda \\sim \\delta x $ \uff0c$ \\sim $\u7b49\u4ef7\u7684\u610f\u601d<\/p>\n\n\n\n

$\\delta x $\u5c31\u662f\u6307\u975e\u5e38\u5c0f\u7684\u5c3a\u5ea6\uff0c\u6240\u4ee5\u53ef\u4ee5\u5199\u6210\u8fd9\u4e2a\u6837\u5b50\uff0c<\/p>\n\n\n\n

$$\\delta x \\delta p \\sim \\hbar$$<\/p>\n\n\n\n

\u5f53\u63a2\u6d4b\u7c92\u5b50\u7684\u52a8\u91cf\u8db3\u591f\u9ad8\u65f6\uff0c\u76f8\u5bf9\u8bba\u6548\u5e94\u5c31\u4f1a\u662f\u4e3b\u8981\u7684\uff0c\u8fd9\u65f6\u63a2\u6d4b\u7c92\u5b50\u7684\u52a8\u91cf\u53ef\u4ee5\u8fd1\u4f3c\u770b\u4f5c<\/p>\n\n\n\n

$$ p= \\frac{E}{c} $$<\/p>\n\n\n\n

\u8fd9\u65f6\u5019\u7684\u4e0d\u786e\u5b9a\u6027\u5173\u7cfb\u5c31\u662f $$\\delta x E \\sim \\hbar c $$<\/p>\n\n\n\n

\u770b\u4e0a\u53bb\u53ef\u4ee5\u63a2\u6d4b\u7684\u8ddd\u79bb\u5c31\u662f\u65e0\u7a77\u5c0f\u7684\uff0cE\u80fd\u65e0\u7a77\u5927\u5417\uff1f\u4f3c\u4e4e\u9677\u5165\u4e86\u6b7b\u5faa\u73af\u3002<\/p>\n\n\n\n

\u6211\u4eec\u77e5\u9053\u4e24\u4e2a\u8d28\u91cf\u4e3aM\u7684\uff0c\u8ddd\u79bb\u4e3ar\u7684\u7c92\u5b50\uff0c\u8fd9\u4e2ar\u5c31\u662f\u4e4b\u524d\u7684$\\delta x$\u4ed6\u4eec\u4e4b\u95f4\u7684\u5f15\u529b\u52bf\u80fd\u4e3a$ E_p= -G\\frac{M^2}{r} \\times r=-G\\frac{M^2}{r} $<\/p>\n\n\n\n

\u7528\u80fd\u91cf\u8868\u8fbe\u4e3a\uff0c\u4e5f\u5c31\u662f\u628a$E=Mc^2$\u5e26\u5165$ E_p= -G\\frac{M^2}{r} $ \u5f97\u5230<\/p>\n\n\n\n

$$G \\frac{E^{2}}{r c^{4}}$$<\/p>\n\n\n\n

\u5728\u76f8\u5bf9\u8bba\u4ee5\u53ca\u91cf\u5b50\u529b\u5b66\u4e2d\u9700\u8981\u4e00\u4e2a\u7cfb\u7edf\u7684\u603b\u80fd\u91cf\u662f\u975e\u8d1f\u7684\uff0c\u6240\u4ee5\u8ddd\u79bb\u4e0d\u80fd\u65e0\u9650\u53d8\u5c0f\uff0c\u6700\u591a\u52bf\u80fd\u7684\u7edd\u5bf9\u503c\u548c\u52a8\u80fd\u76f8\u5f53$ G \\frac{E^{2}}{r c^{4}} \\sim E $\u6574\u7406\u53ef\u5f97\uff1a<\/p>\n\n\n\n

$$ r \\sim G\\frac{E}{c^4} $$<\/p>\n\n\n\n

$$ E= \\hbar \\nu = \\hbar \\frac{c}{ \\lambda} = \\hbar \\frac{c}{ r}$$ <\/p>\n\n\n\n

\u8fd9\u91cc\u9700\u8981\u8bf4\u660e $\\lambda $ \u7b49\u4ef7\u4e8e r \u6574\u7406\u53ef\u5f97\uff0c\u90a3\u4e48\u8fd9\u4e2a\u9ed1\u6d1e\u7684\u534a\u5f84\u5c31\u662f\u666e\u6717\u514b\u957f\u5ea6\u3002\u53f2\u74e6\u897f\u534a\u5f84\u548c\u5eb7\u666e\u987f\u6ce2\u957f\u7ed3\u5408\u5c31\u662f\u666e\u6717\u514b\u957f\u5ea6(G\/c)\u3002\u5f0f\u4e2d\u662f\u7ea6\u5316\u666e\u6717\u514b\u5e38\u6570\uff0cG\u4e3a\u91cd\u529b\u5e38\u6570\uff0cc\u4e3a\u5149\u901f\u3002<\/p>\n\n\n\n

$$r \\sim \\sqrt{\\frac{G \\hbar}{c^{3}}}=l_{p}$$<\/p>\n\n\n\n

\u8ba1\u7b97\u5f97\uff1a$l_{p}= 1.616229\u00d710^{-35}m$<\/p>\n\n\n\n

\u4ee3\u5165\u8ba1\u7b97\u540e\u8fd8\u53ef\u4ee5\u5f97\u5230\u8fbe\u5230\u8fd9\u4e2a\u7a0b\u5ea6\u6240\u9700\u8981\u7684\u80fd\u91cf\u4e5f\u5c31\u662f\u666e\u6717\u514b\u80fd\u91cf\u8868\u8fbe\u5f0f\uff1a<\/p>\n\n\n\n

$$\\sqrt{\\frac{\\hbar c^{5}}{G}}=E_{p}$$<\/p>\n\n\n\n

<\/p>\n\n\n\n

<\/p>\n\n\n\n

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