2003x3fxefxc4x29x5cxc6x7fxc1xb5xfex66xe5xc6xc1x4b March 11, 2003 x31x98x4bxa335xa9xa4 1.x58x4aΨ1xdaΨ2xb4x2cx98x4ex58x1bxb9x9exc5xbdx99x90xa7x1bxfcx87x29 1). xa7x82x1bx82x35x53x5c Ψ = aΨ1 +bΨ2; (a, bxb4x7exea)xa7xb4xc4xf7x76xd3x18x1bxb9x9exc5xbdx99x90xa7xba 2). x65x2dΨ0 = Ψ1Ψ2xa7x5cx40x8fΨ0xb4xc4xf7x76xd3x18x1bxb9x9exc5xbdx99x90 xa7xba 2.x9fxfex83xd3x1bxfcx87xe2x66xa9x4fx33xb0xddxd8xd3x1bxfcx87x98x91xc3x81x1dxb3xb2 xa5xa7xc1xafxc4xb3xb2xa5xe2x66x1bxc4x15x55xfex24xa7x84xb4xb0xb3xb2xa5x1bxc4x15 x55xfex24xba 3. 1). x5cxb4xc4x40xa3xf9x6ex87xddxa 0 @ 0 11 0 1 A 0 @ 0 ?ii 0 1 A 0 @ 1 00 ?1 1 A x33xfex66xe5xc6xa5xa6x82xa1x8fx9fx6fxba 2). x8cx5bx7fx17xa7[?x; ?p] = iˉh x8fxfex66xe5xc6xa5x81xc4x1dx1bxe9xb4x27x58 xa3xf9x70?xxda?pxa9x4fxb4xa0x98x8excexdaxc4xfex8excexa4x5cxb4xc4x50x1axexc4 xfe?Lx; ?Ly; ?Lzx83x6dx1bxe9xb4x27x58xbax9ex15xd1x35! 3). x9ex8ex98x65[ [?Lx; ?Ly]; ?Lz]+[ [?Ly; ?Lz]; ?Lx]+[ [?Lz; ?Lx]; ?Ly] =? 1 x31x13x4bxa320xa9xa4 x6bx98x87x56xb3xb2 V0 = 8> >>> >>>> >< >>> >>>> >>: 1 x < 0 ?V0 0 < x < a 0 a < x < 2a ?V0 2a < x < 3a 1 2V0 3a < x : xf9x70V0 > 0xa7xc1x15xd1x88xabx8dx53xc5xbcxeax1bxdcx6ex2fxaaxb1x39xebx1ax88xabx8d x1bx3ex2ex5ex87xa3xd8x37xe4x4exa6x29xa4 x31x6ex4bxa325xa9xa4 x3fx33xfex21x3ex7cxa5x1bx13x91x91x3ex14x8x66x1bx4dx97xeexfex8f ?H = 1 2m(p 2 x +p 2 y)+ 1 2m! 2(x2 +y2)+eEx: (x35xb5xd9xa5x3ex7cx72xddExb4x7exeaxa7ex8fxc4x1dx3exd6) 1.xa6xd1xd9x55x3fx22 2.x3ex7cEx1bx8cx2xacx17x29x9fx6fx4bx8fxba x31x6fx4bxa320xa9xa4 x58x4ax72x6x66xa2x77x8ax64x98x87x3axd8xdax64x3ex66xfex21xa9xd9x33x8cxbbx8fa0x1bxa5 x53xa4x7cxa4xa7x40x6fxd9xd1x13xb3x8cx4cxabx8f V(r) = 8< : Ze2 r ? r R; r < a0 0; r > a0: xd9xa5R = a20Ze2,xc1x5exc0xcx43x71xa6x87xa9xd1x13x1fxa1x22 x31xcax4bxa322xa9xa4 x7fxc4x6bx13xadx53xdcx67x64xddx1bxe2x66xa7xd9x7bxbfxc4x15jAi;jBixe9x41x75xd3x98x55 xfeE0xa7x3d H0jAi = E0jAi H0jBi = E0jBi xc1xa6x83x70x8ax5e H0 = a2(jAihAj+jBihBj)+ b2(jAihBj+jBihAj) xdaxe5x1bx55xfex3fx14x22 xa3x4axabxb5hAjBi = 0;H0AA = hAjH0jAi;H0AB = hAjH0jBi￠￠￠) x31x38x4bxa328xa9xa4 ?H = 1 2m(p 2 x +p 2 y)+ 1 2m! 2(x2 +y2)+J?!S1 ￠?!S2; J ? ˉh! ?!S 1; ?!S 2x4cxabxe2x661xdaxe2x662x1bx67x5ex8excexa3x4ax32xb5x87x7fxc4x1cxd3x35x6x6exa7 xd8x37x5ex87x36xd8xa4 1.xa6x64xfexe3x4dx97xeexfexa3x15x1bx67x5ex8f1/2xe2x66x58xdax1bxc4x15x55xfexdaxc4 x15xc5xbcxeax22 2.xa6x64xfexe3x4dx97xeexfexa3x15x1bx67x5ex8f1xe2x66x58xdax1bxc4x15x55xfexdaxc4x15 xc5xbcxeax22