{"id":871,"date":"2012-06-03T23:58:57","date_gmt":"2012-06-03T15:58:57","guid":{"rendered":"http:\/\/www.hsyyf.me\/?p=871"},"modified":"2012-06-03T23:58:57","modified_gmt":"2012-06-03T15:58:57","slug":"%e6%b0%a2%e5%8e%9f%e5%ad%90%e5%be%84%e5%90%91%e6%b3%a2%e5%87%bd%e6%95%b0%e6%95%b0%e5%80%bc%e6%b1%82%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.hsyyf.me\/?p=871","title":{"rendered":"\u6c22\u539f\u5b50\u5f84\u5411\u6ce2\u51fd\u6570\u6570\u503c\u6c42\u89e3"},"content":{"rendered":"<p>\u6c22\u539f\u5b50\u955c\u50cf\u6ce2\u51fd\u6570\u65b9\u7a0b\uff08\u5316\u4e3a\u539f\u5b50\u5355\u4f4d\u5236\uff09\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\">$$\\left( -\\frac{d^2}{2dr^2}+\\frac{l(l+1)}{2r^2}-\\frac{1}{r} \\right) P(r)=EP(r)$$<\/p>\n<p>\u5176\u8fb9\u754c\u6761\u4ef6\u4e3a\uff1aP(0)=0,P(\u221e)=0\uff0cl\u4e3a\u8f68\u9053\u91cf\u5b50\u6570\uff0cl=0,1,2,3\u2026\u5206\u522b\u5bf9\u5e94s\u8f68\u9053\uff0cp\u8f68\u9053\uff0cd\u8f68\u9053\uff0cf\u8f68\u9053\u3002\u3002\u3002<\/p>\n<p>\u672c\u610f\u4f7f\u7528Nomerov\u65b9\u6cd5\uff0c\u6570\u503c\u6c42\u89e3\u5f84\u5411\u6ce2\u51fd\u6570\uff0c\u4f46\u662f\u5bf9\u4e8er=0\u5904\u6709\u5947\u70b9\uff0c\u6b64\u5904\u91c7\u7528\u5dee\u5206\u6cd5\u6c42\u89e3\u8fd9\u4e2a\u4e8c\u9636\u7ebf\u6027\u975e\u9f50\u6b21\u5fae\u5206\u65b9\u7a0b\u7684\u672c\u5f81\u503c\u95ee\u9898\u3002Nomerov\u6709\u4e94\u9636\u7cbe\u5ea6\uff0c\u800c\u5dee\u5206\u53ea\u6709\u4e8c\u9636\u7cbe\u5ea6\uff0c\u51fa\u73b0\u7684\u95ee\u9898\u7a0d\u540e\u518d\u8bf4\u3002<\/p>\n<p>\u7531\u4e8e\u6709\u65e0\u7a77\u8fd9\u4e2a\u5947\u70b9\uff0c\u6b64\u5904\u53bb\u53d6\u65e0\u7a77\u7b49\u4e8e40\u4f5c\u4e3a\u622a\u77ed\u70b9\uff08l=0\u65f6\uff0cr=40\u4e2a\u73bb\u5c14\u534a\u5f84\u65f6\u6ce2\u51fd\u6570\u5df2\u8d8b\u8fd1\u4e8e\u96f6\uff09\u3002\u5229\u7528\u6253\u9776\u6cd5\u786e\u5b9a\u672c\u5f81\u80fd\u91cfE\u3002<br \/>\n\u7a0b\u5e8f\uff1a\uff08\u6b64\u5904\u53d6l=1\uff0c\u6c42p\u8f68\u9053\u57fa\u6001\u6ce2\u51fd\u6570\uff0c\u7a0b\u5e8f\u672a\u505a\u5f52\u4e00\u5316\u5904\u7406\uff09<br \/>\n<code lang=\"fortran\">Module Number<br \/>\nINTEGER,PARAMETER :: N=10000<br \/>\nINTEGER,PARAMETER :: K=5000<br \/>\nINTEGER,PARAMETER :: L=1<br \/>\nREAL(8),PARAMETER :: h=400.0d0\/N<br \/>\nINTEGER :: i,j<br \/>\nEND<\/p>\n<p>PROGRAM main<br \/>\nuse Number<br \/>\nREAL(8) :: JF,Sum,Y(0:N),E1,E2,Yk,Yk1,EPS<br \/>\nOPEN(10,FILE='Data.txt')<br \/>\nY(0)=0.d0<br \/>\nY(1)=0.005d0<br \/>\nEPS=5.d0<br \/>\nYk=0.d0<br \/>\nE1=-1.d0<br \/>\nE2=0.d0 <\/p>\n<p>j=2<br \/>\nCALL CF(Y,E1)<br \/>\nYk1=Y(k)<br \/>\nE=-1.d0\/(2*J*j)<\/p>\n<p>DO WHILE (ABS(E1-E2)>1.d-6)<br \/>\n    E=(E1+E2)\/2.d0<br \/>\n    PRINT*,E<br \/>\n    CALL CF(Y,E)<br \/>\n    IF (ABS(Y(k)-Yk)<EPS)THEN\n        EXIT\n    ENDIF\n    IF ((Y(k)-Yk)*(Yk1-Yk)<0) THEN\n        E1=E\n    ELSE\n        E2=E\n    ENDIF\nENDDO\nCALL CF(Y,e)\n\nSum=JF(Y(0:K))\nPRINT*,E !,Y(k)\/SQRT(Sum)\nDO i=0,K\n    WRITE(10,*)i*h,Y(i)\nENDDO\nEND\n\nSUBROUTINE CF(Y,e)\nUSE Number\nreal(8) :: r,Y(0:N)\nDO i=1,N-1\n    r=i*h\n    Y(i+1)=2*Y(i)+h*h*(L*(L+1)\/(r*r)-2.d0\/r-2*e)*Y(i)-Y(i-1)\nENDDO\nEND\n\nFUNCTION JF(Y)\nUSE Number\nREAL(8) :: JF,Y(0:k)\nJF=0.d0\nDO i=0,k-1\n    JF=JF+(Y(i)**2+Y(i+1)**2)*h\/2.d0\nENDDO\nEND<\/code><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c\u5982\u56fe\uff1a<a href=\"http:\/\/www.hsyyf.me\/wp-content\/uploads\/2012\/06\/Data.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-873\" title=\"Data\" src=\"http:\/\/www.hsyyf.me\/wp-content\/uploads\/2012\/06\/Data.png\" alt=\"\" width=\"336\" height=\"271\" srcset=\"https:\/\/www.hsyyf.me\/wp-content\/uploads\/2012\/06\/Data.png 336w, https:\/\/www.hsyyf.me\/wp-content\/uploads\/2012\/06\/Data-300x241.png 300w\" sizes=\"auto, (max-width: 336px) 100vw, 336px\" \/><\/a><\/p>\n<p>E=-0.1250<\/p>\n<p>\u660e\u663e\uff0c\u572825\u4e2a\u73bb\u5c14\u534a\u5f84\u4e4b\u540e\uff0c\u6ce2\u51fd\u6570\u5f00\u59cb\u4e0a\u7fd8\uff0c\u4e3b\u8981\u539f\u56e0\u5728\u4e8e\u622a\u77ed\u70b9\u7684\u9009\u53d6\u6709\u95ee\u9898\u3002\u81f3\u4e8e\u4e3a\u4ec0\u4e48\u6ca1\u80fd\u8fbe\u523040\u4e2a\u73bb\u5c14\u534a\u5f84\uff0c\u4e3b\u8981\u539f\u56e0\u5219\u662f\u5dee\u5206\u6cd5\u7cbe\u5ea6\u4e0d\u591f\u3002\u800c\u80fd\u91cf\u5219\u57fa\u672c\u63a5\u8fd1\u89e3\u6790\u503c\u3002<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6c22\u539f\u5b50\u955c\u50cf\u6ce2\u51fd\u6570\u65b9\u7a0b\uff08\u5316\u4e3a\u539f\u5b50\u5355\u4f4d\u5236\uff09\u4e3a\uff1a $$\\left( -\\frac{d^2}{2dr^2}+\\frac [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[16],"tags":[108,122,103],"class_list":["post-871","post","type-post","status-publish","format-standard","hentry","category-16","tag-fortran","tag-122","tag-103"],"_links":{"self":[{"href":"https:\/\/www.hsyyf.me\/index.php?rest_route=\/wp\/v2\/posts\/871","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hsyyf.me\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.hsyyf.me\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.hsyyf.me\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hsyyf.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=871"}],"version-history":[{"count":0,"href":"https:\/\/www.hsyyf.me\/index.php?rest_route=\/wp\/v2\/posts\/871\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.hsyyf.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=871"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.hsyyf.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=871"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.hsyyf.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=871"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}