Re: [理工] [近物]-量子力學

[kagato (包)]

※ 引述《lionichiro (阿暐~~!)》之銘言：
: 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

如果他只給兩分就直接寫x<0位能∞所以沒有穿透,穿透係數=0,反射係數=1

有錯誤請多指教.@@
: 拜託了!!

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◆ From: 118.171.100.66
※ 編輯: kagato          來自: 118.171.100.66       (12/08 22:10)
推 gogogoclark:嗯?(1)式後面應該是D*exp(ika)
→ kagato:把k都改k3好了~_~  謝謝指正
推 gogogoclark:若令k=k3 那就要改成令D=1 求C了
→ gogogoclark:最後反射係數之分母要換成(c*)*c
推 youmehim:k2裡面的V少乘了2m