{"id":2240,"date":"2022-02-24T17:59:01","date_gmt":"2022-02-24T08:59:01","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2240"},"modified":"2024-07-11T09:45:51","modified_gmt":"2024-07-11T00:45:51","slug":"%e3%83%9e%e3%83%ab%e3%82%b5%e3%82%b9%e3%81%ae%e4%ba%ba%e5%8f%a3%e3%83%a2%e3%83%87%e3%83%ab","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f\/%e3%83%9e%e3%83%ab%e3%82%b5%e3%82%b9%e3%81%ae%e4%ba%ba%e5%8f%a3%e3%83%a2%e3%83%87%e3%83%ab\/","title":{"rendered":"\u30de\u30eb\u30b5\u30b9\u306e\u4eba\u53e3\u30e2\u30c7\u30eb"},"content":{"rendered":"<h3>\u5fae\u5206\u65b9\u7a0b\u5f0f\u304c\u51fa\u3066\u304f\u308b\u73fe\u5b9f\u4e16\u754c\u306e\u4e00\u5834\u9762\uff1a\u30de\u30eb\u30b5\u30b9\u306e\u4eba\u53e3\u30e2\u30c7\u30eb<\/h3>\n<p>\u4eba\u53e3\u5909\u5316\u306e\u3057\u304b\u305f\u3092\u660e\u3089\u304b\u306b\u3057\uff0c\u5c06\u6765\u306e\u5909\u5316\u3092\u4e88\u6e2c\u3059\u308b\u30e2\u30c7\u30eb\u3092\u5b9a\u5f0f\u5316\u3059\u308b\u3053 \u3068\u306f\u5b9f\u793e\u4f1a\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u91cd\u8981\u306a\u554f\u984c\u3067\u3042\u308b\u3002\u3053\u3053\u3067\u306f\uff0c\u307e\u305a\u30de\u30eb\u30b5\u30b9\u306e \u300c\u4eba\u53e3\u8ad6\u300d\u306b\u66f8\u304b\u308c\u305f\u30a2\u30a4\u30c7\u30a2\u3092\u7d39\u4ecb\u3059\u308b\u3002<!--more--><\/p>\n<ul>\n<li><strong>\u3010\u53c2\u8003\u3011<\/strong> \u300c<a href=\"https:\/\/www.nippyo.co.jp\/shop\/book\/1240.html\">\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u6570\u5b66\u30e2\u30c7\u30eb\u3092\u4f5c\u308d\u3046 \u30d0\u30fc\u30b8\u30a7\u30b9\uff0c\u30dc\u30ea\u30fc\u8457\uff0c\u65e5\u672c\u8a55\u8ad6\u793e<\/a>\u300d<\/li>\n<\/ul>\n<p id=\"yui_3_17_2_1_1645692262100_1448\">\u6642\u523b \\(t\\) \uff08\u305f\u3068\u3048\u3070\u300c\u5e74\u300d\u3068\u3057\u3066\u3082\u3088\u3044\uff09\u306b\u304a\u3051\u308b\u3042\u308b\u56fd\u306e\u7dcf\u4eba\u53e3\u3092 \\(N(t)\\) \u3068\u3059\u308b\u3002\u77ed\u3044\u6642\u9593\u9593\u9694 \\(dt\\) \u306b\u304a\u3051\u308b\u51fa\u751f\u6570\u3068\u6b7b\u4ea1\u6570\u306f\uff0c\u3068\u3082\u306b\u305d\u306e\u6642\u70b9\u3067\u306e\u7dcf\u4eba\u53e3\u3068\u6642\u9593\u9593\u9694\u306b\u6bd4\u4f8b\u3059\u308b\u304b\u3089\uff0c<br id=\"yui_3_17_2_1_1645692262100_1449\" \/><br id=\"yui_3_17_2_1_1645692262100_1450\" \/>$$\\mbox{\u51fa\u751f\u6570} = \\alpha N dt, \\quad<br id=\"yui_3_17_2_1_1645692262100_1451\" \/>\\mbox{\u6b7b\u4ea1\u6570} = \\beta N dt<br id=\"yui_3_17_2_1_1645692262100_1452\" \/>$$<br id=\"yui_3_17_2_1_1645692262100_1453\" \/><br id=\"yui_3_17_2_1_1645692262100_1454\" \/>\u3057\u305f\u304c\u3063\u3066\uff0c\u6642\u9593\u9593\u9694 \\(dt\\) \u3067\u306e\u4eba\u53e3\u306e\u5897\u52a0 \\(dN\\) \u306f<br id=\"yui_3_17_2_1_1645692262100_1455\" \/><br id=\"yui_3_17_2_1_1645692262100_1456\" \/>$$dN = \\alpha N dt &#8211; \\beta N dt = \\gamma N dt, \\quad\\mbox{\u305f\u3060\u3057}\\<br id=\"yui_3_17_2_1_1645692262100_1457\" \/>\\gamma \\equiv \\alpha &#8211; \\beta<br id=\"yui_3_17_2_1_1645692262100_1458\" \/>$$<br id=\"yui_3_17_2_1_1645692262100_1459\" \/><br id=\"yui_3_17_2_1_1645692262100_1460\" \/>\u3053\u308c\u306f\u5fae\u5206\u65b9\u7a0b\u5f0f<br id=\"yui_3_17_2_1_1645692262100_1461\" \/><br id=\"yui_3_17_2_1_1645692262100_1462\" \/>$$\\frac{dN}{dt} = \\gamma N<br id=\"yui_3_17_2_1_1645692262100_1463\" \/>$$<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1465\">\u3067\u3042\u308a\uff0c\u5909\u6570\u5206\u96e2\u6cd5\u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1466\">\u307e\u305a\uff0c<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1467\">$$ \\frac{dN}{N} = \\gamma \\,dt $$<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1468\">$$ \\int \\frac{dN}{N} = \\gamma \\int dt $$<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1469\">\u984c\u610f\u3088\u308a \\( N &gt; 0 \\) \u3060\u304b\u3089\uff0c<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1470\">$$ \\ln N = \\gamma t + C $$<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1471\">$$ \\therefore N(t) = e^C\\, e^{\\gamma t } \\equiv C&#8217;\\,e^{\\gamma t }$$<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1472\">\u3053\u3053\u3067\uff0c\u7a4d\u5206\u5b9a\u6570 \\(C\\) \uff08\u3042\u308b\u3044\u306f \\(C&#8217;\\) \u3092\uff0c\u521d\u671f\u6761\u4ef6\u3092\u4f7f\u3063\u3066\u3042\u3089\u308f\u3059\u3002\u3053\u3053\u3067\u306e\u521d\u671f\u6761\u4ef6\u3068\u3057\u3066\uff0c\\( t = t_0 \\) \uff08\u5e74\uff09\u306e\u3068\u304d\u306e\u4eba\u53e3\u3092 \\(N_0\\) \u3068\u3059\u308b\u3002\u3059\u306a\u308f\u3061\uff0c<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1473\">\\[ N(t_0) = N_0 = C&#8217;\\, e^{\\gamma\\,t_0} \\]<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1474\">\u3053\u308c\u304b\u3089\uff0c\\( C&#8217; = N_0\\, e^{-\\gamma \\,t_0} \\) \u3068\u306a\u308a\uff0c\u6700\u7d42\u7684\u306b\u3002<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1476\">$$ N(t) = N_0 e^{\\gamma (t &#8211; t_0)} $$<\/p>\n<p id=\"yui_3_17_2_1_1645692262100_1398\">\u30de\u30eb\u30b5\u30b9\u30fb\u30e2\u30c7\u30eb\u306f\uff0c\\(\\gamma &gt; 0\\) \u306e\u5834\u5408\u306b\u306f\u4eba\u53e3\u306e\u969b\u9650\u306a\u3044\u5897\u52a0\uff08\u6307\u6570\u95a2\u6570\u7684\u5897\u52a0\uff09\u3092\u4e88\u6e2c\u3059\u308b\u3002\u3057\u304b\u3057\uff0c\u5b9f\u969b\u306b\u306f\u3044\u308d\u3044\u308d\u306a\u8981\u56e0\u306b\u3088\u308a\uff0c\u3053\u306e\u3088\u3046\u306a\u7121\u5236\u9650\u306a\u5897\u52a0\u306f\u7d9a\u304b\u306a\u3044\u3002\u4ee5\u4e0b\u306e\u30b0\u30e9\u30d5\u3092\u53c2\u7167\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2243 size-full\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maru.svg\" alt=\"\" width=\"600\" height=\"480\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5fae\u5206\u65b9\u7a0b\u5f0f\u304c\u51fa\u3066\u304f\u308b\u73fe\u5b9f\u4e16\u754c\u306e\u4e00\u5834\u9762\uff1a\u30de\u30eb\u30b5\u30b9\u306e\u4eba\u53e3\u30e2\u30c7\u30eb <\/p>\n<p>\u4eba\u53e3\u5909\u5316\u306e\u3057\u304b\u305f\u3092\u660e\u3089\u304b\u306b\u3057\uff0c\u5c06\u6765\u306e\u5909\u5316\u3092\u4e88\u6e2c\u3059\u308b\u30e2\u30c7\u30eb\u3092\u5b9a\u5f0f\u5316\u3059\u308b\u3053 \u3068\u306f\u5b9f\u793e\u4f1a\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u91cd\u8981\u306a\u554f\u984c\u3067\u3042\u308b\u3002\u3053\u3053\u3067\u306f\uff0c\u307e\u305a\u30de\u30eb\u30b5\u30b9\u306e \u300c\u4eba\u53e3\u8ad6\u300d\u306b\u66f8\u304b\u308c\u305f\u30a2\u30a4\u30c7\u30a2\u3092\u7d39\u4ecb\u3059\u308b\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f\/%e3%83%9e%e3%83%ab%e3%82%b5%e3%82%b9%e3%81%ae%e4%ba%ba%e5%8f%a3%e3%83%a2%e3%83%87%e3%83%ab\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":2224,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2240","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u5fae\u5206\u65b9\u7a0b\u5f0f\u304c\u51fa\u3066\u304f\u308b\u73fe\u5b9f\u4e16\u754c\u306e\u4e00\u5834\u9762\uff1a\u30de\u30eb\u30b5\u30b9\u306e\u4eba\u53e3\u30e2\u30c7\u30eb 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