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1、InfiniteSquareWellPotentialU(x)0,xU,xa0x-a0ah2d即(x)2|lxdx2xaah2d即(x)2|lxdx2+U中(x)=砂(x)0UT阿(x)-!W(x)=0卩2=2(U0-E)dx2h2a一卩2中(x)=0卩2=0dx2h2中(x)=Ce卩x+De-卩xxaxT+8,中(x)hastobelimited.C=0,中(x)=De-卩xaUT,中(x)T0中(x)=00xaUT,中(x)T0中(x)=00Conclusion:Foranyxinoutsideofthewell中(x)=0h2d2,(x)2dx2二E,(x)即E+a2,(x)二0a2二2
2、已dx2h2中(x)二Asinax+Bcosaxx二a,中(a)二Asinaa+Bcosaa二0x二-a,中(一a)二-Asinaa+Bcosaa二0Asinaa二0Bcosaa二0兀A二0,B0,cosaa二0naa二n一,n二1,3,5.中(x)二Bcosax2.兀B二0,A0,sinaa二0naa二n一,n二2,4,6.中(x)二Asinaa2n0otherwise中(x)二0foreverywhere.兀兀22E兀2兀2h2n2aa二nna2a2二n2na2二nnE二一24h2424a2兀2h2n2E二,n二1,2,3,4,5.n2p(2a)2中(x)nn兀Asin-2a0”乜,(x)
3、2dx二1nA2gFinalConclusions:+asin2an兀2a,1x+a)dx二1nA二-a中(x)二ja2a0兀2h2n2E二,n二1,2,3,4,5.n2p(2a)2FinalConclusions:中(x)=n1.n,/、smx+a),a2a0E=,n=1,2,3,4,5.n2(2a)22x,x+a0X2a兀2h2n21.n兀,sinx,a2a中(x,),n12n,1,2,3,4,5.中(x),n中(x),nv2.n兀sinx,LLxL,兀2h2n22卩(L)2n,1,2,3,4,5.迥isin0xL,兀2h2n2,n,1,2,3,4,5.2(L)2中(x),30x(Lx),
4、”C中(x)Lnnn,1中(xM(x),中(x)30x(Lx),”C中mmL)nn,1m(x)中m“中(x)中(x)dx,“中m0“中(x)中(x)dx,Cmnm0(x).x(Lx)dxC,“中(x)彳。x(Lx)dxLnnL5(x).x(Lx)dx,”CLnn,1nn030x(Lx)dx,“Wsin巴xL、工L030x(Lx)dx,空-1(1)nLn3兀31-30.1.1xsinnxdx,一sinnx一xcosnxCn2nx2sinnxdx(2sinnxnxcosnx)cosnxCn2n3x(Lx)中(x),30u中(x),nsin巴x,0xLLxL,兀2h2n2n,1,2,3,4,5.2(
5、L)2中(x),J30x(Lx),C中(x)VL5nnn=1/、迈.nKr厂兀2h2n2中(x)sinx,0xL,E,,nQLn2p(L)2n,1,2,3,4,5.C,空21兀3C2,99.85%1(、迈.兀x中(x)=-=sin14llK22E12g-C,02C2,02/、忑.2kx中(x)=-=sin24LL2k22E,2PL2XC,更327兀3C2,014%3/、忑.3kx中(x),-=sin34LL9兀22E,32pL2-C,04C2,04/、迥.4kx中(x)=-=sin44LL8K22E,4PL2XC,疸2553兀3C2,6.3910-3%5/、近.5kx中(x),-sin54ll
6、25k22E,52pL-2n孚1-(-1)n“1(1)nn6兀6iInfiniteSquareWellPotentialECBFinijaaStartpositionwfthzerospeedAFinitequantumwellcos-npestatessin-txrpestatesEU00UoU(x)IEnergyIIIIIdiicretespectrumcotpd:2j=G-=-时从./?=JhiQ-町口rrd22mdz2wavefunctions:爭=M+W叭nl-a/2n=1,35,-expff,(z-d/2)1zd!2(-1)“-expczn(z-f?/2)Jzd/2X=$J1+wt,J=/7thth?QWsjieuzthenergyjiiii富=ur=LR.cgion1RtHjLOU2R帕檢3XWhatifHlBoaTieakdioftbsIsk聊也尊1*昭血&