作者microball (迎向 七月 盛夏)
看板ZooStudy
标题Re: [转录]90学年度第2学期林敏聪普物期末考
时间Wed Jun 11 22:48:39 2003
※ 引述《magicfx (Photoshop 画油画)》之铭言：
: 5.Please write down the Schroedinger equation for a guantum well system with
: length L and infinite deep potential well. (10%)
: Solve the Schroedinger equation and obtain the quantized energy and the
: related wave function. (20%)
V = 0 ,0<x<L
= infinite ,otherwise
Schrodinger eq.: d^2 ψ 8π^2 mE
-------- + -----------ψ = 0
dx^2 h^2
solve: ψ= a cos Sx + b sin Sx
where S = (8π^2 mE /h^2) ^(1/2) ...(8π^2 mE /h^2 的开根号)
a,b is free real number
boundery condition: x=0, ψ(0)=0 ...1
x=L, ψ(0)=0 ...2
let a=0 ,so ψ(L)= b sin SL = 0 ...3
because b must not be 0, only when SL = nπ satisfied 3.
we can know that E= n^2 (h^2) / 8mL^2
it is easy to hshow that b= (2/L)^(1/2)
ps. It is arbitrary to choose sine or cosine function when let a=0 or b=0
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◆ From: 61.226.114.155
※ 编辑: microball 来自: 61.226.114.155 (06/11 22:50)
※ 编辑: microball 来自: 61.226.114.155 (06/11 22:50)