\u7ba1\u7406\u4eba\u304c\u4ee5\u524d\u6295\u7a3f\u3057\u305f\u8a18\u4e8b(\u9759\u6b62\u8cea\u91cf\u30a8\u30cd\u30eb\u30ae\u30fc<\/a>)\u304c\u53c2\u8003\u306b\u306a\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/p>\n\n\n\n
\n\n\n\n
\u5149\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306f$E=h\\nu$\u3001\u904b\u52d5\u91cf\u306e\u6642\u9593\u6210\u5206\u306f$p=\\frac{E}{c}=\\frac{h\\nu}{c}$\u3068\u8868\u3055\u308c\u307e\u3059\u3002
\u3053\u3053\u3067\u3001$h$\u306f\u30d7\u30e9\u30f3\u30af\u5b9a\u6570\u3001$\\nu$\u306f\u5149\u5b50\u306e\u5468\u6ce2\u6570\u3067\u3059\u3002<\/p>\n\n\n\n
\u8a08\u7b97\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5909\u6570\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u305d\u308c\u305e\u308c\u306e\u95a2\u4fc2\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n $$ ${E_e}^2$\u3068$\\boldsymbol{p_e}^2$\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n $$ $E^2=c^2p^2$\u3001${E’}^2=c^2{p’}^2$\u3001$EE’=cp\\cdot cp’=c^2 pp’$\u3001$E-E’=cp-cp’=c(p-p’)$\u306a\u306e\u3067\u3001<\/p>\n\n\n\n $$ \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n ${p_e}^2$\u306b\u3064\u3044\u3066\u306f\u3001<\/p>\n\n\n\n $$ \u3068\u306a\u308a\u307e\u3059\u3002 $u^\\mu$\u30924\u5143\u901f\u5ea6\u3068\u3057\u305f\u3068\u304d\u3001<\/p>\n\n\n\n $$ \u3068\u306a\u308a\u307e\u3059\u3002 $$ \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n 4\u5143\u904b\u52d5\u91cf$p^\\mu$\u306f<\/p>\n\n\n\n $$ \u3068\u8868\u3055\u308c\u307e\u3059\u3002 $p^2$\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001<\/p>\n\n\n\n $$ \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u4e00\u65b9\u3067\u3001$p^\\mu=\\left( \\frac{E}{c},p^i \\right)$\u306e\u65b9\u306e\u5b9a\u7fa9\u3092\u7528\u3044\u308b\u3068\u3001<\/p>\n\n\n\n $$ \u3068\u306a\u308a\u307e\u3059\u3002 $$ \u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \u5f0f2\u3068\u5f0f3\u304c\u7b49\u3057\u3044\u306e\u3067\u3001<\/p>\n\n\n\n $$ \u3088\u308a\u3001<\/p>\n\n\n\n $$ \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u4ee5\u4e0a\u3088\u308a\u3001${E_e}^2=c^2{p_e}^2+m^2c^4$\u306a\u306e\u3067\u3001\u5f0f1\u3088\u308a\u3001<\/p>\n\n\n\n $$ \u3053\u3053\u3067\u3001$\\lambda=\\frac{c}{\\nu}=c\\cdot\\frac{h}{cp}=\\frac{h}{p}$\u3068\u3059\u308b\u3068\u3001$p=\\frac{h}{\\lambda}$\u306a\u306e\u3067\u3001<\/p>\n\n\n\n $$ \u3057\u305f\u304c\u3063\u3066\u3001\u6ce2\u9577\u306e\u5909\u5316$\\Delta\\lambda$\u306f\u3001<\/p>\n\n\n\n $$ \u3068\u306a\u308a\u307e\u3059\u3002 <\/p>\n","protected":false},"excerpt":{"rendered":" X\u7dda\u306a\u3069\u306e\u5149\u5b50\u304c\u7269\u8cea\u306b\u3088\u3063\u3066\u6563\u4e71\u3055\u308c\u308b\u3068\u6ce2\u9577\u304c\u5909\u5316\u3057\u307e\u3059\u3002\u3053\u306e\u73fe\u8c61\u3092\u30b3\u30f3\u30d7\u30c8\u30f3\u6563\u4e71(Compton scattering)\u3068\u547c\u3073\u307e\u3059\u3002 \u3053\u3053\u3067\u306f\u3001\u5149\u5b50\u304c\u96fb\u5b50\u306b\u885d\u7a81\u3059\u308b\u5834\u5408\u306e\u6ce2\u9577\u306e\u5909\u5316\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002 \u3053\u306e\u8a18\u4e8b\u306e\u5185\u5bb9\u306f\u524d\u63d0\u3068 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[36],"tags":[],"class_list":["post-1844","post","type-post","status-publish","format-standard","hentry","category-36"],"_links":{"self":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1844","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1844"}],"version-history":[{"count":13,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1844\/revisions"}],"predecessor-version":[{"id":1861,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1844\/revisions\/1861"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1844"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1844"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\u5909\u6570<\/th> \u610f\u5473<\/th><\/tr><\/thead> $E, \\boldsymbol{p}$<\/td> \u5165\u5c04\u3057\u305f\u5149\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u904b\u52d5\u91cf<\/td><\/tr> $E’, \\boldsymbol{p’}$<\/td> \u6563\u4e71\u3055\u308c\u305f\u5149\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u904b\u52d5\u91cf<\/td><\/tr> $E_e, \\boldsymbol{p_e}$<\/td> \u8df3\u306d\u98db\u3070\u3055\u308c\u305f\u96fb\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u904b\u52d5\u91cf<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n ![\"\"](\"https:\/\/daba-no-heya.com\/wp-content\/uploads\/2026\/07\/\u885d\u7a81\u524d.png\")
![\"\"](\"https:\/\/daba-no-heya.com\/wp-content\/uploads\/2026\/07\/\u885d\u7a81\u5f8c.png\")
\\left\\{ \\begin{aligned} &E+mc^2=E’+E_e \\\\ &\\boldsymbol{p}+\\boldsymbol{0}=\\boldsymbol{p’}+\\boldsymbol{p_e} \\end{aligned} \\right.
$$<\/p>\n\n\n\n
\n\\begin{align}\n{E_e}^2&=(E-E’+mc^2)^2 \\\\\n&=E^2+{E’}^2-2EE’+2Emc^2-2E’mc^2+(mc^2)^2 \\\\\n&=E^2+{E’}^2-2EE’+2mc^2(E-E’)+(mc^2)^2\n\\end{align}\n
$$<\/p>\n\n\n\n
\n{E_e}^2=c^2p^2+c^2{p’}^2-2c^2pp’+2mc^3(p-p’)+m^2c^4 \\tag{1}\n
$$<\/p>\n\n\n\n
\\begin{align} {p_e}^2&=(\\boldsymbol{p}-\\boldsymbol{p’})^2 \\\\ &=p^2-2\\boldsymbol{p}\\cdot\\boldsymbol{p’}+{p’}^2 \\\\ &=p^2+{p’^2}-2pp’\\cos\\theta \\end{align}
$$<\/p>\n\n\n\n
$\\theta$\u306f\u5149\u5b50\u306e\u6563\u4e71\u89d2\u3067\u3059\u3002<\/p>\n\n\n\n
\n\n\n\n
\n\\begin{align}\nu^2&\\equiv\\eta_{\\mu\\nu}u^\\mu u^\\nu \\\\\n&=-\\left( \\frac{dct(\\tau)}{d\\tau} \\right)^2+\\left( \\frac{dx(\\tau)}{d\\tau} \\right)^2+\\left( \\frac{dy(\\tau)}{d\\tau} \\right)^2+\\left( \\frac{dz(\\tau)}{d\\tau} \\right)^2 \\\\\n&=\\left( \\frac{ds}{d\\tau} \\right)^2 \n\\end{align}\n
$$<\/p>\n\n\n\n
\u3053\u3053\u3067\u3001$ds^2=-(cd\\tau)^2$\u306a\u306e\u3067\u3001$ds=icd\\tau$\u3088\u308a\u3001<\/p>\n\n\n\n
u^2=\\left( \\frac{ds}{d\\tau} \\right)^2=(ic)^2=-c^2
$$<\/p>\n\n\n\n
\np^\\mu=(\\gamma mc,\\gamma mv^i)=\\left( \\frac{E}{c},p^i \\right)\n
$$<\/p>\n\n\n\n
\u3053\u3053\u3067\u3001$\\gamma$\u306f\u30ed\u30fc\u30ec\u30f3\u30c4\u56e0\u5b50\u3067\u3059\u3002<\/p>\n\n\n\n
\n\\begin{align}\np^2&\\equiv\\eta_{\\mu\\nu}p^\\mu p^\\nu \\\\\n&=\\eta_{\\mu\\nu}(mu^\\mu)(mu^\\nu) \\\\\n&=m^2\\eta_{\\mu\\nu}u^\\mu u^\\nu \\\\\n&=m^2u^2 \\\\\n&=-m^2c^2 \\tag{2}\n\\end{align}\n
$$<\/p>\n\n\n\n
p^2=\\eta_{\\mu\\nu}p^\\mu p^\\nu=-\\left( \\frac{E}{c} \\right)^2+\\delta_{ij}p^i p^j \\tag{3}
$$<\/p>\n\n\n\n
\u3053\u3053\u3067\u306e$\\delta_{ij}p^i p^j$\u306f<\/p>\n\n\n\n
\n\\delta_{ij}p^i p^j=\\sum_{i=1}^3\\left( p^i \\right)^2\n
$$<\/p>\n\n\n\n
\n-\\left( \\frac{E}{c} \\right)^2+\\delta_{ij}p^ip^j=-m^2c^2\n
$$<\/p>\n\n\n\n
\nE^2=c^2\\delta_{ij}p^ip^j+m^2c^4\n
$$<\/p>\n\n\n\n
\n\n\n\n
\n\\begin{align}\n&c^2p^2+c^2{p’}^2-2c^2pp’+2mc^3(p-p’)+m^2c^4=c^2{p_e}^2+m^2c^4 \\\\\n&c^2(p^2+{p’}^2-2pp’\\cos\\theta)=c^2p^2+c^2{p’}^2-2c^2pp’+2mc^3(p-p’) \\\\\n&c^2p^2+c^2{p’}^2-2c^2pp’\\cos\\theta=c^2p^2+c^2{p’}^2-2c^2pp’+2mc^3(p-p’) \\\\\n&2c^2pp’-2c^2pp’\\cos\\theta=2mc^3(p-p’) \\\\\n&pp'(1-\\cos\\theta)=mc(p-p’)\n\\end{align}\n
$$<\/p>\n\n\n\n
\n\\begin{align}\n&\\frac{h}{\\lambda}\\frac{h}{\\lambda’}(1-\\cos\\theta)=mc\\left( \\frac{h}{\\lambda}-\\frac{h} {\\lambda’} \\right) \\\\\n&\\frac{h^2}{\\lambda\\lambda’}(1-\\cos\\theta)=mch\\frac{\\lambda’-\\lambda}{\\lambda\\lambda’} \\\\\n&h(1-\\cos\\theta)=mc(\\lambda’-\\lambda)\n\\end{align}\n
$$<\/p>\n\n\n\n
\n\\Delta\\lambda=\\lambda’-\\lambda=\\frac{h}{mc}(1-\\cos\\theta)\n
$$<\/p>\n\n\n\n
\u3053\u3053\u306b\u767b\u5834\u3059\u308b\u4fc2\u6570$\\frac{h}{mc}\\approx 2.43\\times 10^{-12} \\text{m}$\u306f\u96fb\u5b50\u306e\u30b3\u30f3\u30d7\u30c8\u30f3\u6ce2\u9577(Compton wavelength)\u3067\u3059\u3002<\/p>\n\n\n\n