第三章习题课详解教学文稿.doc

第三章习题课详解教学文稿 第三章习题课详解)()(),()(),()(),()(),(),()(),(),()(),()()()()(),()(),(),(,),(),(,),()(,),(;,;,;,)(,)()(.1020000200000000220000000000000000000t t t t U t t t U tt t U t t t Ut t U t t t Ut t UtttU ttt bttUttt UttUt a t a W tt UttUt at attU Wtt attUtt att atta WttataWt ai iiii iiiiii iiii iii?，而对于纯相来说，?101111212101111111110111132)1 (2)1()34(cos3)2(sin)2(sincos3sin sin cos sin),()cos3sin sincos sin()() (1)(), (3)2()2()()cos3sin sincos sin()(,cos,sin sin,cos sin)()3()(,sincos;cos,sin,sin)(.15Y Yi Yiie ee erf r r rx bLxr frYiY YrYYrr frrr xrz ry rxr fz yx xi eYe Ye Yai iiiiii?的本征函数。 的本征值为是2222222222222222222222222120)() (12)()()() (2)( (12),()()1()(1sin1)(sinsin11) (1)()2(),()()()(.111)1191(1,111)1191(1,119)1193(0mrrRdrdr rRmE r Vr ERr RrVr Rrrr Rrrr mFrrR llrr Rrrrr rrrrE rVmF rR xcP mPmP mlll?）在球坐标中表示为代入薛定谔方程将被找到的概率为被找到的概率为被找到的概率为?m m j jmm jjm jm jm jk m jm jm jm jk m jm jkm jm jm jm jkm jm jm jm jkm jn nn nmn njn n n n n nkkn njn nkn nnnnna annk,1,1,)(,)1)(1(,1)(,1)1)(1(,2,21,1,1211,1)1)(1(,.19?表象下的矩阵表示为在，转化为并将，令为总量子数的降算符。 同理是总量子数的升算符，增加，即使总量子数同时增加和使显然?1010202020202,12,1,1,11,0,1,11,)1)(,2,)(.22)1(?mmmii iiJmjiJ Jmjm jJ mj Jmjm jmjmjmjJiJ JJiJ J JiJ JJ ayyjyyy xyx?1010xx121202040202410202020xx020202041)(,!)()(20ii iiiiiiJnJ iebynnyiJy?0121222123)!12()(!2)(1,.2,1,0,)(,.;2,1,0,02020202021020202020211010xx121nn ymmyiJymy ynyyniJmiJemJJn JJii iiiiiiJy?sin)()1(cos1)!12()1(!2)1(1xx122?y ynnnymm myJi JnJimJ?2cos12sin2cos12sincos2sin2cos12sin21cos1020202020sin211010xx121)cos1(sin)cos1()()(,sin)cos1()(1,)exp(,)() (2)(2)(?ii iiiIJiJI dmjJiJm jmjiJm jd cyyjm myyyjm m?212-2)(2,0)()(21,2