北京科技大學(xué)部分量子力學(xué)作業(yè)試題匯總

2.910mK）T3max：根據(jù)氫原子的玻爾理論，氫原子的電離能是，即：E13.61.61019J198s，c，m，151734T15373KT4X1110X10X1110m103.010ms//3.010，18Hzcc86.6310h2.010h34JsJ5，6.63104.11015eVs/ph/hph34Js9.110，31kg24me/7.010ms1vpm6ep2E17J2me(,,)maVxyzxa;ya;za(,,)Vxyz,為122x,y,zE,,xyz2m，x,y,zXxYyZzEEEExyznx2222d2XxEnnnEXxXxx22a2maax2x2xYynyd22222EYyYy2；；Ey2maa2a2yy2yZz222d22nzZzEEZzz2z2a2m2aaz2z23/2nxnxnxxyz,,sinsinsinyzxaaaa22，,1,2,3,...nnn,En2n2n22mamnl2xyzxyz,;,rsrsrr,,ASAss11z22z121z2z322E2E01112marsrs,;,,,xyz,,xyz1AA11z22z1111111122223yzxyzx111222aaaaaaa1ssss21z21z2zz322EE201112marr,,,xyz,,xyz1S121111111122223yzxyzx111222aaaaaaaVa0EV00ex。0VxVxxkx2mVa，,k0x0x20kx0ka02ka2,4,6......0ka02ka,3,5......0222nkan,n3......V002ma222V02ma2m（V0EVV000的躍起處考慮還存在勢：）的散射，即電子所受勢能為0()xx0(x)V(x)(x)，這里(x)iVx00j在0x0處的透射系數(shù)T，outxjinj；Rrefjin）定態(tài)薛定諤方程：E；2d2V(x)(x)2mdx022mEVx2mxx02m()()0,0，dx2()()V(x)(x)E在x020202mE0，x0xxx,0k2k222m(EV)x,0k2k202()x,0x,0xeikxAeikxikxikx(),0x,0xBeikxxikx0x1AB1AB2mk2mB1BABB22kkm21：AB21iB2mkk1ik12k2km1ii12k12kk1Amm1i112k12k2k2kkki*kkkjj,Aj,22*jB2mxxinmremoutm2m2m12ii12kkj2kkk2kRA2reinmj12m12kk1212kk2k2kkjkkT2Boutjk22m1in12k2kk2mk1212kk2kk1RT2m2112k2kk??xx。pxix?,??xpx?????,?，L,L?，）L,L?xpxxyyz??L,L?xz??????????]2（L,LL,LL,LL,L?LLLL2222zxyyzzxxyz?????????1】?,?2】，，3】L,LiLL,LiLL,LLxpixxxyzyzxzy2L,L0z2L2,1,，,,lmlllmLlmmlmz，LLiL，，LLiLLLLxyxyz符，使本征值減少i）和是否為厄密算符）計算LLLz?LlmLlm?,?,l,mLL,lm?l,mLL,lm??LiLL2L，L?LLiL2Lxyxyzzll1m(m1)lmlm1ll1mml,mLLl,m?2222LiLL2LL?LLiL2Lxyxyzzll1m1mlmlm1ll1mml,mLLl,m?222211,lm,lm,，,LlmlmlmLlmlmlm,,?，?，?，?；L2LlmLLL2L2zxyxy122。LLLL,x2xyy2：,1lm,，,,LlmllLlmmlm2zLL,x，,LLiLLLLLyiLzyzyzzyxiLLLLLmLL0xyzzyyy0LLxy2iLLLLLLLLLLLLLLLiLLLLxyzzyxyzxzyxyxzyzyx2iLLLLLLLyyxzzyx2ll1L2L2L2L2L2L2xyxyz1222Lll1mL22xyLL2LL2L22L2xxxxxx2LL2yy1212m22222LLll1m，,LL2xyxy22222110lllmmllmmlmlm1222LL,xmlLLyxy??（l1,LL2z33x8Yei8r1133z4r3x8YY4103ei8r11??L,LY,Y,Y2x111011?YLx10,,,xzxyzyzxrr,,3y1112iYYY83xr21111210111YY104r211113y111iY11YY8r221121011??,LL2x1211211Y10Y11Y1121YY1021111111YYY11211210211111?YLx10211。p2m2x2，與xpH2m2m1x,pi；引入算符：x,P，線性變換：Qpm11Q,aQ。計算：對易關(guān)系：a22Q,P?a,a?,aaa?a,aa?將用,Haa）,,1[,aaQPiaaaaa],aaap2m2x21212），，nHaan0,1,2...E2m2n2mx2p2H?。Haa122m2??aa?mi?mixxpap,a2m2m????axpa?]??，??，??，xpx022；??p222。xp4??m】???,?ixaaaa2m2】?0|?|00xx?0|?|00pp?xx0|?|0222mm2?pp0|?|022m2,???,?x2p2222m242n1m2n122n12222,??22?,?2m244?nzn?n函數(shù)（取1zzn：?nsin,0,cos，?naabb01；sin221，1，112211在。；10zzn|2|2。222211，，，a,ba,a1b,b1，bS,ba,ba,b,0baabaaSa；求證：SzabbS,S，S,S2）定義算符：SS2zz122Nb1NabS2S2SSSSN22z：b22,SS,aa,ba,babaabbabaaabbbbaa2aS222za,a22,ab,bb,babaSSzabbba2bS222aab2S,,bb,,,ababSSabba2aa2bbaab2zab222S2abbaab422222abb1abaa1baabb2ab24222224ab2aa2bbaabb2ab4422aabb2aa2bb2ab4222N2aabbaabbN14222和HHHHHH00000bE，HH1H0E00b2EEbE0H1bEE2EEbdet0HE1bEE21224bEEEE1EE1222將EEEREE1122b2121/21/222，1111EERRRRRR22，1，，EERR22和SSSssz12SS2和zHs12s1222S2S,,0z12A0S20SzS2s2s2Hsss12121223422222JEss2234412T022343J24ssE22412SHHH。H0so022ppxHyHyx02m2msop表示電子自旋運動與軌道運動的耦合：泡利矩陣：Hpxysoyx01100i101001，，，1001xyiz電子波函數(shù)可表示為自旋運動波函數(shù)與軌道運動波函數(shù)的直積形式：11kAyikr,。ksksikxkeeyxzzAA10，。ss2021zzszH02HHH0sok011ikx,kkikr，eky,ekkxy0AA2k202m2k2H02m2k202mk0akkb,ka,bk0bpp2aa2myxkEk，pbbp22myx2k2Ek2myx0k2k2E2myx2k0e2k22k22kk，EkkEk222，tankxy2m2mxykk2e，0）HJSSSSSSJ122313SSS2222SSSSSSSSS1231232122313231212，；定義：121212312123，求：||?，，，?SSSStotS2|S|?|S|2z1231tot12tot21tot1||?，?，H?SHz2tot212844。3J2,f4J9412ESS243ttJ,f4423||||，，S2S22||||SSzz41tot12tot2221tot12tot234HHJ21122A，AaaaaAaAa*aaAa**a0，0