{"id":6451,"date":"2022-04-27T16:38:21","date_gmt":"2022-04-27T08:38:21","guid":{"rendered":"https:\/\/qt.ntu.edu.tw\/qoa\/?p=6451"},"modified":"2025-05-15T13:50:47","modified_gmt":"2025-05-15T05:50:47","slug":"202204_qt_uncertainty_principle","status":"publish","type":"post","link":"https:\/\/qt.ntu.edu.tw\/qoa\/202204_qt_uncertainty_principle\/","title":{"rendered":"\u6e2c\u4e0d\u6e96\u539f\u7406 Uncertainty Principle"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"6451\" class=\"elementor elementor-6451\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7ba1b10 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7ba1b10\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-1c689da\" data-id=\"1c689da\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-198107d elementor-widget elementor-widget-text-editor\" data-id=\"198107d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><small><a href=\"https:\/\/qt.ntu.edu.tw\/qoa\">Home<\/a> \/ <a href=\"https:\/\/qt.ntu.edu.tw\/qoa\/knowledge\/knowledge_map\/\">\u77e5\u8b58\u5730\u5716<\/a> <\/small><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4f3aa05\" data-id=\"4f3aa05\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-331bbd7 elementor-align-right elementor-widget elementor-widget-button\" data-id=\"331bbd7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"#\" id=\"printer\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"fas fa-print\"><\/i>\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">\u5217\u5370<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ffc279c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ffc279c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-37e0b01\" data-id=\"37e0b01\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d5bcc63 printer elementor-widget elementor-widget-text-editor\" data-id=\"d5bcc63\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>\u4f5c\u8005\uff1a\u9673\u6137\u5ef7<br \/>\u7de8\u8f2f\uff1a\u9ec3\u6587\u6ed4\uff5c\u91cf\u5b50\u7dda\u4e0a\u5b78\u9662\u7279\u7d04\u7de8\u8f2f (\u81fa\u7063\u5927\u5b78\u5316\u5b78\u7cfb\u78a9\u58eb)<br \/>\u5be9\u95b1\uff1a\u912d\u539f\u5fe0 \uff5c\u81fa\u7063\u5927\u5b78\u5316\u5b78\u7cfb\u6559\u6388<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-737c68d printer elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"737c68d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3c5d52c\" data-id=\"3c5d52c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fd98516 elementor-widget elementor-widget-text-editor\" data-id=\"fd98516\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>1. <strong>\u524d\u8a00<\/strong><\/h3><p>\u5b78\u904e\u91cf\u5b50\u529b\u5b78\u7684\u540c\u5b78\uff0c\u4e00\u5b9a\u807d\u904e\u6d77\u68ee\u5821(Werner Heisenberg, 1901-1976)\u65bc1927\u5e74\u63d0\u51fa\u7684\u6e2c\u4e0d\u6e96\u539f\u7406(the uncertainty principle\uff0c\u6216\u7a31\u4e0d\u78ba\u5b9a\u6027\u539f\u7406)\u3002\u76f8\u4fe1\u5927\u5bb6\u5c0d\u6e2c\u4e0d\u6e96\u539f\u7406\u7684\u7406\u89e3\u5927\u6982\u662f \u2014 \u82e5\u60f3\u5f97\u77e5\u4e00\u500b\u7269\u9ad4\u7684\u78ba\u5207\u4f4d\u7f6e\uff0c\u5247\u6703\u56e0\u70ba\u5728\u6e2c\u91cf\u904e\u7a0b\u4e2d\u7684\u884c\u70ba\uff0c\u4f7f\u7269\u9ad4\u7684\u901f\u5ea6\u5931\u6e96\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u4f46\u6211\u5011\u61c9\u8a72\u63db\u500b\u89d2\u5ea6\u770b\uff0c\u5176\u5be6\u6e2c\u4e0d\u6e96\u539f\u7406\u548c\u300c\u6e2c\u91cf\u300d\u4e26\u6c92\u6709\u95dc\u4fc2\uff0c\u800c\u662f\u4e00\u500b\u55ae\u7d14\u7531\u7269\u8cea\u7684\u300c\u6ce2\u7c92\u4e8c\u8c61\u6027\u300d\u6240\u5c0e\u81f4\u7684\u5fc5\u7136\u7d50\u679c\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9f40073 elementor-widget elementor-widget-spacer\" data-id=\"9f40073\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-089701c elementor-widget elementor-widget-image\" data-id=\"089701c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P1-1024x768.png\" class=\"attachment-large size-large wp-image-6831\" alt=\"\" srcset=\"https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P1-1024x768.png 1024w, https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P1-300x225.png 300w, https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P1-768x576.png 768w, https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P1-1536x1152.png 1536w, https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P1-2048x1536.png 2048w, https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P1-600x450.png 600w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">\u57161. \u6e2c\u4e0d\u6e96\u539f\u7406\u6982\u5ff5\u5716\u3002<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9df5f7a elementor-widget elementor-widget-text-editor\" data-id=\"9df5f7a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>\u6e2c\u4e0d\u6e96\u539f\u7406\u63cf\u8ff0\u4e86\u7269\u9ad4\u7684\u4f4d\u7f6e\u8207\u52d5\u91cf\u5177\u6709\u4e0d\u78ba\u5b9a\u6027\uff0c\u4e26\u4e14\u5b58\u5728\u4e00\u500b\u6700\u5c0f\u6975\u9650\uff0c\u4f7f\u5f97\u7121\u6cd5\u540c\u6642\u6e96\u78ba\u63cf\u8ff0\u7269\u9ad4\u7684\u4f4d\u7f6e\u8207\u52d5\u91cf\u3002\u9019\u662f\u7531\u65bc\u7269\u8cea\u5177\u6709\u6ce2\u7c92\u4e8c\u8c61\u6027\uff0c\u5176\u4f4d\u7f6e\u8207\u52d5\u91cf\u7684\u4e0d\u78ba\u5b9a\u6027\u5206\u5225\u53cd\u6620\u4e86\u7269\u8cea\u7684\u7c92\u5b50\u6027\u8207\u6ce2\u52d5\u6027\u3002\u7576\u7269\u8cea\u7684\u7c92\u5b50\u6027\u8f03\u660e\u986f\u6642\uff0c\u5176\u5728\u7a7a\u9593\u4e2d\u6703\u5177\u6709\u8f03\u78ba\u5b9a\u7684\u4f4d\u7f6e\uff1b\u7576\u7269\u8cea\u7684\u6ce2\u52d5\u6027\u8f03\u660e\u986f\u6642\uff0c\u5176\u52d5\u91cf\u7684\u78ba\u5b9a\u6027\u6703\u8f03\u9ad8\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-61238ce printer elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"61238ce\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b141ea3\" data-id=\"b141ea3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d57f26e elementor-widget elementor-widget-spacer\" data-id=\"d57f26e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cfd5dce elementor-widget elementor-widget-text-editor\" data-id=\"cfd5dce\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>2. <strong>\u6ce2\u7c92\u4e8c\u8c61\u6027<\/strong><\/h3><p>\u5c0d\u65bc\u7c92\u5b50\u800c\u8a00\uff0c\u6211\u5011\u53ef\u4ee5\u78ba\u5b9a\u5176\u5728\u67d0\u500b\u7279\u5b9a\u6642\u9593\u4e0b\u6703\u5b58\u5728\u65bc\u67d0\u500b\u7279\u5b9a\u4f4d\u7f6e\uff0c\u7136\u800c\u6ce2\u537b\u7121\u6cd5\u6709\u4e00\u500b\u56fa\u5b9a\u65bc\u4e00\u500b\u9ede\u7684\u4f4d\u7f6e\uff0c\u56e0\u70ba\u6ce2\u7684\u5f62\u6210\u4e00\u5b9a\u6709\u8cf4\u65bc\u7a7a\u9593\u4e0a\u8a31\u591a\u9ede\u4e4b\u9593\u5177\u6709\u540c\u8abf\u6027\u7684\u904b\u52d5\u3002\u7531\u65bc\u6ce2\u5177\u6709\u9019\u7a2e\u975e\u5b9a\u57df(delocalized)\u7684\u7279\u6027\uff0c\u6211\u5011\u5fc5\u9808\u4ee5\u6ce2\u51fd\u6578\u4f86\u63cf\u8ff0\u4e4b\uff0c\u4e5f\u5c31\u662f\u628a\u6ce2\u5728\u7a7a\u9593\u4e0a\u6bcf\u4e00\u9ede\u7684\u632f\u5e45\u63cf\u8ff0\u51fa\u4f86\u3002\u8207\u5176\u8aaa\u7269\u8cea\u4e00\u5b9a\u5177\u6709\u6ce2\u548c\u7c92\u5b50\u5169\u7a2e\u6027\u8cea\uff0c\u4e0d\u5982\u8aaa\u7c92\u5b50\u5c31\u662f\u6ce2\uff0c\u6216\u8005\u8aaa\u7c92\u5b50\u53ea\u662f\u6ce2\u7684\u4e00\u7a2e\u6bd4\u8f03\u5b9a\u57df(localized)\u7684\u7279\u4f8b\u3002\u6839\u64da\u5fb7\u5e03\u7f85\u610f (Louis de Broglie, 1892-1987) \u7684\u7269\u8cea\u6ce2(matter wave)\u7406\u8ad6\uff0c\u4e00\u500b\u7269\u9ad4\u7684\u7269\u8cea\u6ce2\u662f\u4e00\u7a2e\u6a5f\u7387\u6ce2\uff0c\u5176\u6ce2\u9577\u03bb\u7531\u5f0f1\u6240\u63cf\u8ff0\uff1a<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bb8eacd elementor-widget elementor-widget-text-editor\" data-id=\"bb8eacd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<strong>\u03bb = \u210e \/ \ud835\udc5d\u3000\u3000\u5f0f1<\/strong>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fb77ff2 elementor-widget elementor-widget-spacer\" data-id=\"fb77ff2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-72bd5d4 elementor-widget elementor-widget-text-editor\" data-id=\"72bd5d4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>\u5176\u4e2d \u210e \u662f\u666e\u6717\u514b\u5e38\u6578 (\u7d046.626 X 10 <sup>-34<\/sup>) \ud835\udc71\u2027\ud835\udc60\uff0c\u800c \ud835\udc91 \u5247\u4ee3\u8868\u7269\u9ad4\u7684\u52d5\u91cf(momentum\uff0c\u7b49\u65bc\u7269\u9ad4\u7684\u8cea\u91cf\u8207\u901f\u5ea6\u7684\u4e58\u7a4d)\u3002\u7576\u7269\u9ad4\u7684\u8cea\u91cf\u5f88\u5927\u6216\u901f\u5ea6\u5f88\u5feb\u6642\uff0c\u7269\u8cea\u6ce2\u6ce2\u9577\u5c31\u77ed\u5230\u7121\u6cd5\u6e2c\u91cf\uff0c\u6545\u65bc\u5de8\u89c0\u4e16\u754c\u7684\u65e5\u5e38\u751f\u6d3b\u4e2d\u96e3\u4ee5\u89c0\u5bdf\u5230\u7269\u9ad4\u7684\u6ce2\u52d5\u6027\uff1b\u4f46\u82e5\u7269\u9ad4\u7684\u8cea\u91cf\u5f88\u5c0f\uff0c\u5982\u96fb\u5b50\u7b49\u5fae\u89c0\u4e16\u754c\u7684\u7c92\u5b50\uff0c\u7269\u8cea\u6ce2\u6ce2\u9577\u5c31\u8db3\u4ee5\u88ab\u6e2c\u5f97\uff0c\u6545\u7c92\u5b50\u7684\u6ce2\u52d5\u6027\u65bc\u5fae\u89c0\u4e16\u754c\u4e2d\u624d\u80fd\u986f\u800c\u6613\u898b\uff0c\u5982\u96fb\u5b50\u7684\u5e72\u6d89\u548c\u7e5e\u5c04\u689d\u7d0b\u7b49\u5be6\u9a57\u3002\u00a0\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8b31454 printer elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8b31454\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-fe01e36\" data-id=\"fe01e36\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4645476 elementor-widget elementor-widget-spacer\" data-id=\"4645476\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d658934 elementor-widget elementor-widget-text-editor\" data-id=\"d658934\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>3. \u6e2c\u4e0d\u6e96\u539f\u7406<\/h3><p>\u4e86\u89e3\u4e86\u6ce2\u7c92\u4e8c\u8c61\u6027\uff0c\u73fe\u5728\u8981\u4f86\u8ac7\u8ac7\u6e2c\u4e0d\u6e96\u539f\u7406\u3002\u5047\u8a2d\u6709\u4e00\u500b\u7d14\u7cb9\u7684\u6ce2\uff0c\u6211\u5011\u53ef\u4ee5\u85c9\u7531\u6ce2\u9577\u6c42\u5f97\u52d5\u91cf\uff0c\u4f46\u7121\u6cd5\u78ba\u5b9a\u5b83\u7684\u4f4d\u7f6e\uff0c\u90a3\u6211\u5011\u8a72\u5982\u4f55\u5275\u9020\u51fa\u4e00\u500b\u540c\u6642\u662f\u6ce2\u53c8\u5177\u6709\u7c92\u5b50\u6027\u7684\u72c0\u614b\uff0c\u5f9e\u800c\u589e\u52a0\u5176\u5728\u4f4d\u7f6e\u4e0a\u7684\u78ba\u5b9a\u6027\u5462\uff1f\u7b54\u6848\u662f\u9760\u6ce2\u7684\u758a\u52a0(superposition)\u3002\u900f\u904e\u6ce2\u7684\u758a\u52a0\uff0c\u6211\u5011\u53ef\u4ee5\u5c07\u539f\u4f86\u975e\u5b9a\u57df\u7684\u6ce2\u8b8a\u5f97\u5728\u7a7a\u9593\u4e0a\u6bd4\u8f03\u96c6\u4e2d(\u6216\u8005\u8aaa\u66f4\u50cf\u7c92\u5b50\u822c\u5728\u7a7a\u9593\u4e2d\u6709\u78ba\u5b9a\u7684\u4f4d\u7f6e)\u3002 \u5982\u57162\u6240\u793a\uff0c\u900f\u904e\u6578\u500b\u4e0d\u540c\u6ce2\u9577\u7684\u6b63\u5f26\u6ce2(\u85cd\u8272\u66f2\u7dda)\u758a\u52a0\uff0c\u53ef\u4ee5\u5f97\u5230\u4e00\u500b\u5728\u7a7a\u9593\u4e2d\u6bd4\u8f03\u5b9a\u57df\u7684\u6ce2\u5f62(\u7d05\u8272\u66f2\u7dda)\u3002\u9019\u662f\u56e0\u70ba\u6ce2\u8207\u6ce2\u4e4b\u9593\u6703\u4e92\u76f8\u5e72\u6d89\uff0c\u9760\u8fd1\u4e2d\u5fc3\u90e8\u5206\u7684\u6ce2\u56e0\u70ba\u76f8\u4f4d\u4e00\u81f4(\u898b\u865b\u7dda\u4f4d\u7f6e)\uff0c\u6ce2\u6703\u4e92\u76f8\u52a0\u6210\u8b93\u632f\u5e45\u589e\u52a0\uff0c\u800c\u9060\u96e2\u4e2d\u5fc3\u7684\u6ce2\u76f8\u4f4d\u6f38\u8da8\u4e0d\u540c\uff0c\u56e0\u6b64\u9019\u90e8\u5206\u7684\u6ce2\u6703\u4e92\u76f8\u62b5\u6d88\uff0c\u7e3d\u9ad4\u800c\u8a00\u4fbf\u7522\u751f\u6bd4\u8f03\u5b9a\u57df\u7684\u6548\u679c\uff0c\u9019\u6a23\u7531\u591a\u500b\u6ce2\u758a\u52a0\u5f97\u5230\u7684\u5c40\u57df\u6ce2\u578b\uff0c\u88ab\u7a31\u4f5c\u4e00\u500b\u300c\u6ce2\u5305\u300d\u3002\u7531\u65bc\u758a\u52a0\u7684\u7279\u6027\uff0c\u6ce2\u7684\u4f4d\u7f6e\u548c\u52d5\u91cf\u7684\u78ba\u5b9a\u6027\u4e26\u4e0d\u80fd\u5920\u540c\u6642\u589e\u52a0\u3002\u7531\u65bc\u5f0f1\u544a\u8a34\u6211\u5011\uff0c\u4e0d\u540c\u6ce2\u9577\u7684\u6ce2\u5177\u6709\u4e0d\u540c\u7684\u52d5\u91cf\uff0c\u56e0\u6b64\u7576\u6ce2\u7684\u52d5\u91cf\u4e0d\u78ba\u5b9a\u6027\u8d8a\u5927\uff0c\u8868\u793a\u53ef\u4ee5\u758a\u52a0\u7684\u6ce2\u53ef\u4ee5\u6709\u66f4\u591a\u4e0d\u540c\u7684\u6ce2\u9577\uff0c\u8b93\u66f4\u591a\u4e0d\u540c\u7684\u6ce2\u758a\u52a0\u5728\u4e00\u8d77\uff0c\u53ef\u4ee5\u7522\u751f\u5728\u7a7a\u9593\u4e0a\u7684\u5206\u4f48\u8d8a\u72f9\u5c0f\u7684\u6ce2\u5305\uff0c\u8868\u793a\u4f4d\u7f6e\u7684\u4e0d\u78ba\u5b9a\u6027\u6e1b\u5c11\u4e86\uff0c\u56e0\u6b64\u7576\u52d5\u91cf\u4e0d\u78ba\u5b9a\u6027\u589e\u52a0\uff0c\u5247\u4f4d\u7f6e\u7684\u4e0d\u78ba\u5b9a\u6027\u53ef\u4ee5\u6e1b\u5c11\uff0c\u76f8\u53cd\u7684\uff0c\u82e5\u6e1b\u5c11\u6ce2\u7684\u52d5\u91cf\u4e0d\u78ba\u5b9a\u6027\uff0c\u4f7f\u5f97\u53ef\u4ee5\u758a\u52a0\u7684\u6ce2\u6578\u91cf\u964d\u4f4e\uff0c\u5c31\u7121\u6cd5\u5f97\u5230\u4f4d\u7f6e\u6e96\u78ba\u7684\u6ce2\u5305\u4e86\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4b6b16b elementor-widget elementor-widget-spacer\" data-id=\"4b6b16b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-04f5874 elementor-widget elementor-widget-image\" data-id=\"04f5874\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1024\" height=\"529\" src=\"https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P2-1-1024x529.png\" class=\"attachment-large size-large wp-image-6836\" alt=\"\" srcset=\"https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P2-1-1024x529.png 1024w, https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P2-1-300x155.png 300w, https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P2-1-768x397.png 768w, https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P2-1-1536x793.png 1536w, https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P2-1-2048x1058.png 2048w, https:\/\/qt.ntu.edu.tw\/qoa\/wp-content\/uploads\/2022\/04\/uncertinty-P2-1-600x310.png 600w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">\u57162. \u900f\u904e\u6b63\u5f26\u6ce2\u758a\u52a0\u5f62\u6210\u5b9a\u57df\u7684\u6ce2\u5f62\u3002<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-13af0c8 elementor-widget elementor-widget-spacer\" data-id=\"13af0c8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-554cd64 elementor-widget elementor-widget-text-editor\" data-id=\"554cd64\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>\u7531\u65bc\u4e0d\u540c\u6ce2\u9577\u7684\u6ce2\u4e4b\u9593\u53ef\u4ee5\u4e92\u76f8\u52a0\u6210\u6216\u62b5\u6d88\uff0c\u4f7f\u5f97\u5404\u500b\u975e\u5b9a\u57df\u7684\u6b63\u5f26\u6ce2\u5728\u758a\u52a0\u5f8c\u53ef\u4ee5\u7522\u751f\u5728\u7a7a\u9593\u4e2d\u96c6\u4e2d\u65bc\u67d0\u500b\u4f4d\u7f6e\u7684\u6ce2\u5f62\u3002\u7136\u800c\u758a\u52a0\u5f8c\u7684\u6ce2\u5f62\u96d6\u7136\u5177\u6709\u6bd4\u8f03\u78ba\u5b9a\u7684\u4f4d\u7f6e\uff0c\u4f46\u76f8\u5c0d\u65bc\u6709\u6e96\u78ba\u52d5\u91cf\u7684\u6b63\u5f26\u6ce2\uff0c\u5176\u52d5\u91cf\u6703\u8b8a\u5f97\u4e0d\u78ba\u5b9a\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-34a4f07 elementor-widget elementor-widget-text-editor\" data-id=\"34a4f07\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>\u5f9e\u4ee5\u4e0a\u7684\u6558\u8ff0\uff0c\u6211\u5011\u53ef\u4ee5\u6b78\u7d0d\u51fa\u4e00\u500b\u7d50\u8ad6\u2014\u7121\u8ad6\u5982\u4f55\uff0c\u90fd\u4e0d\u53ef\u80fd\u540c\u6642\u7cbe\u6e96\u5730\u5f97\u5230\u4e00\u500b\u7c92\u5b50\u7684\u4f4d\u7f6e\u548c\u52d5\u91cf\u3002\u6d77\u68ee\u5821\u5728\u4e00\u756a\u63a8\u7406\u548c\u8a08\u7b97\u5f8c\uff0c\u5f97\u5230\u4e86\u6700\u7d42\u7d50\u8ad6\uff1a<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e58a777 elementor-widget elementor-widget-text-editor\" data-id=\"e58a777\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong><em>\u0394<\/em>\ud835\udc65 \u2027 <em>\u0394<\/em>\ud835\udc5d \u2265 \u210e \/ 4\u03c0 \u3000\u3000\u5f0f2<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3c6df75 elementor-widget elementor-widget-spacer\" data-id=\"3c6df75\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f9f429b elementor-widget elementor-widget-text-editor\" data-id=\"f9f429b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>\u5176\u4e2d\u00a0<em>\u0394<\/em>\ud835\udc65\u548c\u00a0<em>\u0394<\/em>\ud835\udc5d \u5206\u5225\u662f\u4f4d\u7f6e\u548c\u52d5\u91cf\u7684\u6a19\u6e96\u5dee\uff0c\u7531\u65bc\u5169\u8005\u7684\u4e58\u7a4d\u5b58\u5728\u4e00\u500b\u4e0b\u9650\uff0c\u4f7f\u5f97\u5b83\u5011\u4e0d\u80fd\u540c\u6642\u8b8a\u5c0f \uff0c\u9019\u5c31\u662f\u6d77\u68ee\u5821\u7684\u6e2c\u4e0d\u6e96\u539f\u7406\u3002\u7c21\u800c\u8a00\u4e4b\uff0c\u6e2c\u4e0d\u6e96\u539f\u7406\u7684\u7522\u751f\uff0c\u4e00\u5207\u6e90\u65bc\u300c\u6ce2\u300d\u7684\u4e00\u7a2e\u5148\u5929\u7279\u8cea\uff0c\u5f70\u986f\u4e86\u91cf\u5b50\u529b\u5b78\u7684\u6ce2\u52d5\u7279\u6027\uff0c\u8207\u6e2c\u91cf\u7684\u65b9\u5f0f\u6216\u8005\u5be6\u9a57\u7684\u8aa4\u5dee\u662f\u6c92\u6709\u95dc\u806f\u7684\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1a0310a elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"1a0310a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5c6b75d printer elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5c6b75d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c6f8b06\" data-id=\"c6f8b06\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-adc5203 elementor-widget elementor-widget-heading\" data-id=\"adc5203\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">\u8cc7\u6599\u4f86\u6e90<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2c35ed6 elementor-widget elementor-widget-text-editor\" data-id=\"2c35ed6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ol><li><a href=\"https:\/\/zh.wikipedia.org\/wiki\/%E4%B8%8D%E7%A1%AE%E5%AE%9A%E6%80%A7%E5%8E%9F%E7%90%86\" target=\"_blank\" rel=\"noopener\">https:\/\/zh.wikipedia.org\/wiki\/\u4e0d\u78ba\u5b9a\u6027\u539f\u7406<\/a><\/li><li><a href=\"https:\/\/www.ted.com\/talks\/chad_orzel_what_is_the_heisenberg_uncertainty_principle\/transcript?language=zh-tw#t-278766\" target=\"_blank\" rel=\"noopener\">https:\/\/www.ted.com\/talks\/chad_orzel_what_is_the_heisenberg_uncertainty_principle\/transcript?language=zh-tw#t-278766<\/a><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-aa9f7ce elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"aa9f7ce\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-76a46b6\" data-id=\"76a46b6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8865456 elementor-widget elementor-widget-html\" data-id=\"8865456\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t  <!-- jQuery -->\r\n  <script type=\"text\/javascript\" src=\"https:\/\/qt.ntu.edu.tw\/epaper\/pluging\/printer\/jquery.min.js\"><\/script>\r\n\r\n  <!-- printThis -->\r\n\r\n  <script type=\"text\/javascript\" src=\"https:\/\/qt.ntu.edu.tw\/epaper\/pluging\/printer\/printThis.js\"><\/script>\r\n\r\n  <!-- printer -->\r\n  <script>\r\n    $('#printer').on(\"click\", function () {\r\n      $('.printer, .page-title').printThis({\r\n        footer: \"\u00a9 2022\u91cf\u5b50\u958b\u653e\u5b78\u9662\"\r\n      });\r\n    });\r\n\r\n\r\n  <\/script>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\u4f5c\u8005\uff1a\u9673\u6137\u5ef7<br \/>\n\u7de8\u8f2f\uff1a\u9ec3\u6587\u6ed4\uff5c\u91cf\u5b50\u7dda\u4e0a\u5b78\u9662\u7279\u7d04\u7de8\u8f2f<br \/>\n\u5b78\u904e\u91cf\u5b50\u529b\u5b78\uff0c\u4e00\u5b9a\u807d\u904e\u6d77\u68ee\u5821(Werner Heisenberg, 1901-1976)\u65bc1927\u5e74\u63d0\u51fa\u7684\u6e2c\u4e0d\u6e96\u539f\u7406(the uncertainty principle\uff0c\u6216\u7a31\u4e0d\u78ba\u5b9a\u6027\u539f\u7406)&#8230;<\/p>\n","protected":false},"author":3,"featured_media":6831,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[81],"tags":[231],"class_list":["post-6451","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-knowledge-map","tag-231"],"_links":{"self":[{"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/posts\/6451","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/comments?post=6451"}],"version-history":[{"count":177,"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/posts\/6451\/revisions"}],"predecessor-version":[{"id":14065,"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/posts\/6451\/revisions\/14065"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/media\/6831"}],"wp:attachment":[{"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/media?parent=6451"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/categories?post=6451"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qt.ntu.edu.tw\/qoa\/wp-json\/wp\/v2\/tags?post=6451"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}