- #1

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- 0

V(x)=0 for x<-a, x>a; -V

_{0}for -a<x<-b, b<x<a; 0 for -b<x<b

I am asked to show that the eigenvalues conditions may be written in the form:

tan(q(a-b))=qα(1+tanh(αb)/(q

^{2}-α

^{2}tanh(αb))$$

and

tan(q(a-b))=qα(1+coth(αb)/(q

^{2}-α

^{2}coth(αb))$$

for the even and odd solutions, where -E=ħ

^{2}α

^{2}/2m and E+V

_{0}=ħ

^{2}q

^{2}/2m.

I first tried to define the wave function in the various regions, focusing on the positive x-axis only and demanding odd solutions:

Ψ(x)=Ae

^{-αx}for x>a; Bsin(q(x-b)) for b<x<a; Ce

^{-αx}+ De

^{αx}for 0<x<b

Is that correct thus far?