北京大学物理学院-量子力学chap2new

《北京大学物理学院-量子力学chap2new》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、Æ.*!24-$2.1)'/3Yw%>[Bohrkvl.d^b7)v
Vh+i=Heisenberg&Schr¨odingerGZ8r7vrH

uG
w2HkiF
>,
-51Fip,Schr¨odingerk

>pb7k:$EdV121K2122V(x)=Kx=mx=mω0x.(1)22m2℄ukSchr¨odingerVa∂h¯2∂2122ih¯ψ(x,t)=−2ψ(x,t)+mω0xψ(x,t).(2)∂t2m∂x2hV(x)!3j
℄3id

2、−iωtψ(x,t)=ϕ(x)e.(3)Fd'V+ijhh¯2d2122hωϕ¯(x)=Eϕ(x)=−ϕ(x)+mω0xϕ(x).(4)2mdx225mE=¯hωRa5^Vk>9
ukvrhRauh
f

3、x

4、→∞3V(x)→∞dkqAaD
℄ilimϕ(x)=0.(5)

5、x

6、→∞ir-b}ϕ(x)kq
f

7、x

8、→∞3VZ,ah¯2d2122−ϕ(x)+mω0xϕ(x)∼=0.(6)2mdx22℄VkUHa1mω02ϕe(x)=exp±x.(7)2h¯14=*i′2mω01mω

9、02ϕe(x)=±xexp±x.(8)2h¯2h¯,g^+jh2′′mω01mω022mω01mω02ϕe(x)=exp±xx±exp±xh¯2h¯h¯2h¯2∼=mω0exp±1mω0x2x2.(9)h¯2h¯d'V+iahuCUHul
ik;
TDlim

10、x

11、→∞ϕ(x)=0ki1mω02ϕe(x)=exp−x.(10)2h¯r-iz1mω02ϕ(x)=ϕe(x)χ(x)=exp−xχ(x).(11)2h¯gE+i′mω01mω021mω02′ϕ(x)=−xexp−xχ(x

12、)+exp−xχ(x).(12)h¯2h¯2h¯~g.X"2#′′mω02mω01mω02ϕ(x)=x−exp−xχ(x)h¯h¯2h¯mω01mω02′1mω02′′−2xexp−xχ(x)+exp−xχ(x).(13)h¯2h¯2h¯F>d'V+ijh222h¯mω0h¯′′h¯2mω0′χ(x)−χ(x)+xχ(x)=Eχ(x).(14)2mh¯2m2mh¯:l+!2h¯′′′hω¯0χ(x)−hω¯0xχ(x)+E−χ(x)=0.(15)2m2r-i℄VaX∞nχ(x)=Cnx(16)n=02k9E
7

13、d'V+ijhmE>kpYm
o&59Ek:mE
m7!2h¯hω¯02C2+E−C0=0,(17)2m27!2h¯hω¯06C3−hω¯0C1+E−C1=0.(18)2m2q(iuC0&C1uk?&GC0=1&C1=0iYd5~pYmXkmES~j$Eχ(x)
e;<5jhk$E-

14、x

15、→∞3ES7amω0x2χ(x)∼eh¯.(19)℄f

16、x

17、→∞3mω0x2ϕ(x)=ϕe(x)χ(x)∼e2¯h→∞.(20)64Born{$Ek:~=5;(k
℄iAFχ(x

18、)zS

19、x7
o&aw!C2axidhω¯0E0=.(21)2H℄ijhC4=C6=···=0.(22)V3uTDC1=0ijhC3=C5=···=0.(23)5iYjhwb7k3v&k$E
Vl(ikmEW6aC0=0&C1=1Hz1E=E1=1+hω¯0,(24)23.d5jC3=C5=···=0,C4=C6=···=0(25)V3Sp
<fEa1En=n+hω¯0(26)23χ(x)k9E1-zSa

20、x7
5iYjhwb7k>9
~uk>9$E(

21、).ar1mω02mω0ϕn(x)=Anexp−xHnx,(27)2h¯h¯5m,mEaq1/2mω0/h¯An=√.(28)π2nn!5~>9$E
ok;GTDZ∞∗ϕm(x)ϕn(x)dx=δmn.(29)−∞(7FXrkHn(y)Ra}

22、x7
}

23、x7kvn,d-HA513*k

24、)F3h)
qzα=mω0/h¯.b7k)>9$Ea√√2222α−αx2α−αxϕ0(x)=e2,ϕ1(x)=αxe2,π1/4π1/4qα/2α2x222−ϕ2(x)=2αx−1e2.(30)π1/45~

25、$EkXd-HA84*ah
5muHkklrzso
>pfn