量子力学试题精选-B

1.2.803.4.1.2.3.^~r=^~p=4.bH=b~L=5.6.7.8.9.10.bFbG[bF;bG]=0bFbG[bF;bG]6=011.112.13.14.ª15.16.17.18.Ã(r;µ;')(µ;')d­rdr19.bA2=IIbA20.21.22.23.c(p;t)jc(p;t)j2dp24.[^x;^px]=[bLx;bLy]=[bLy;bLz]=25.bA;bB[bA;bB]=26.27.28.29.Ãnlm(r;µ;')=Rnl(r)Ylmµ;'n;l;m30.jÃiF¸bFjÃi231.bF(~r;¡i~r)ª(~r)Rª¤(~r)bFª(~r)dxdydz32.33.ª=q12Y10+q13Y21+cY20ªYlmcLZL2=6~234.35.36.b~SbS2[bS2;bSZ]=bS2[bSx;bSy]=37.38.39.40.ª=264ª1(x;y;z)ª2(x;y;z)375R1¡1jª1j2dxdydzR1¡1¡jª1j2+jª2j2¢dxdydz=41.42.43.ª(~r;t)44.45.46.347.48.49.50.51.52.53.54.55.56.57.58.59.60.61.62.63.xª(x)=A1+ix(1)(2)(3)464.Ã(~r;t)=Aei~(~p¢~r¡Et)65.ª(r;µ;')=12R2;1Y1;0¡p32R2;1Y1;¡1(1)En(2)L2L2(3)zLzzLzLz66.E(0)1;E(0)2bH0bH0H011=H022=b;H012=H021=a(1)bH(0)bH0bH(2)567.SzbSxbSySx=~20B@01101CASy=~20B@0¡ii01CASz(1)bSz(2)bSxbSybSz(3)bSx^SybSz68.E(0)1;E(0)2bH0bH0H011=H022=b;H012=H021=a(1)bH(0)bH0bH(2)69.¢l=§1;¢m=0;§1(1)3s!2s(2)3p!2s(3)3d!2s670.ª=0B@12R21(r)Y11(µ;')¡p32R21(r)Y10(µ;')1CA(1)zLzLz(2)zSzSz(3)c~M=e2¹b~L¡e¹b~SzMz71.U(x)=8:1;(x0)0;(06x6a)¡1;(xa)72.*xª(x)=8:Axe¡¸x;x00;x0¸0(1)(2)(3)773.*bL2bLZbLxbLybLx=~p220BBBB@0101010101CCCCAbLy=~p220BBBB@0¡i0i0¡i0i01CCCCA74.*ª(x)=8:Axe¡¸x;x00;x0¸0(1)(2)R10xme¡®xdx=m®m+175.bH0bHH=0BBBB@E010a0E02ba¤b¤E031CCCCAE01E02E03876.bLxbL2x77.bAbB78.t=0Ã(x)=A£sin2kx+12coskx¤79.^~r=^x~i+^x~j+^x~k=x~i+y~j+z~k^~P=^px~i+^py~j+^pz~k=¡i~³@@x~i+@@y~j+@@z~k´980.^~r=^x~i+^x~j+^x~k=x~i+y~j+z~k^~P=^px~i+^py~j+^pz~k=¡i~³@@x~i+@@y~j+@@z~k´101.2.3.~r¡i~r4.i~@@t~r£^~p=¡i~~r£r5.6.7.8.t~rjª(~r;t)j29.Rª¤ªd¿=1;Rª¤¸0ª¸d¿=±(¸0¡¸)10.11.FermiBose12.¢l=l0¡l=§1;¢m=m0¡m=0;§113.E=hº=~!;~p=h¸~k14.z¹e4s2~2n2l(l+1)~2m~15.¢l=l0¡l=§1;¢m=m0¡m=0;§1;¢s=016.L=mvr=n~;n=1;2;¢¢¢17.Ek=12¹v2m=hº¡W018.Y¤lm(µ;')Ylm(µ;')d­=Y¤lm(µ;')Ylm(µ;')sinµdµd';R2nl(r)r2dr19.§120.21.1122.23.p»p+dp24.i~;i~bLz;i~bLx:25.026.¢xi¢pi¸~2;i=x;y;z27.28.29.n=1;2;¢¢¢;l=0;1;2;¢¢¢;n¡1;m=0;§1;§2;¢¢¢;§l30.jÃibF31.ª(~r)32.33.c=q16;Lz=0;~1234.¢l=§1;¢m=0;§1;¢ms=035.~MS=¡e¹~S36.034~2i~bSz37.Sz=§~2~MS=¡e¹~SMSz=§MB=§e~2¹38.~ML=¡e2¹~L;~MS=¡e¹~S39.40.tSz=~=2t41.42.43.1244.45.46.47.48.49.50.51.52.53.54.55.56.57.58.59.60.61.62.63.(1)Z1¡1A21+x2dx=(2)(3)1364.Ã(~r;t)=Aei~(~p¢~r¡Et)=Aei~(~p¢~r)ei~(¡Et)=Ã(~r)ei~(¡Et)65.66.67.68.69.70.71.72.73.74.75.76.77.78.79.80.14