作者kagato (包)
看板Grad-ProbAsk
标题Re: [理工] [近物]-量子力学
时间Tue Dec 8 22:08:25 2009
※ 引述《lionichiro (阿暐~~!)》之铭言：
: Consider a potential given by U(x)={∞, x<a ; -V, 0<x<a ; 0, x>a} with V>0
: Assume a plane wave of momentum -k(h/2π) is sent from +∞
: Please find the amplitude of reflect wave?
U(x)={∞, x<0 ; -V, 0<x<a ; 0, x>a} (h/2π我用Η表示@@)
Ⅰ 0 Ⅱ a Ⅲ
_____________________________________________________________________
ik3x -ik3x
ψ1 = 0 ψ2 =Acos(k2x)+Bsin(k2x) ψ3 = Cexp + Dexp
__________
√(kΗ)^2 +V
k2=____________ k3 = -k
Η
令入射波C = 1
B.C.
ψ1(0) =ψ2(0) => A=0
ika -ika
ψ2(a) =ψ3(a) , Bsin(k2a) = exp + Dexp __________(1)
ika -ika
ψ'2(a)=ψ'3(a), Bk2*cos(k2a) = ik*exp - Dik*exp ________(2)
i2ka
(1)/(2) 再整理一下可得 exp [ik*tan(k2a) - k2]
D = ____________________
k2 + ik*tan(k2a)
*
v3*D D *
R = ________ = D *D = 1
*
v3*A A
如果他只给两分就直接写x<0位能∞所以没有穿透,穿透系数=0,反射系数=1
有错误请多指教.@@
: 拜托了!!
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◆ From: 118.171.100.66
※ 编辑: kagato 来自: 118.171.100.66 (12/08 22:10)
1F：推 gogogoclark:嗯?(1)式後面应该是D*exp(ika) 12/08 22:57
2F：→ kagato:把k都改k3好了~_~ 谢谢指正 12/08 23:00
3F：推 gogogoclark:若令k=k3 那就要改成令D=1 求C了 12/08 23:16
4F：→ gogogoclark:最後反射系数之分母要换成(c*)*c 12/08 23:28
5F：推 youmehim:k2里面的V少乘了2m 12/09 10:46