Infinite potential well with Delta function inside

[Ace10]

Hello guys,

I need some serious help for the solution of a problem in Q.M, I'm not so sure if I deal with it properly..

Consider an infinite potential well with the traits:

V(x):∞, for x>a and x<-a

V(x):λδ(x), for -a≤x≤a

What happens to the energy levels due to the existence of the delta-potential and what is the value of λ so the ground state energy is zero?

I think that due to the delta potential if λ>0 the energy spectrum has increased values..

Can anybody think about it and untangle me? I would be grateful.

Thanks in advance

 

[hilbert2]

First you should find out how to solve the energy eigenstates for the normal delta function potential, read these:

http://en.wikipedia.org/wiki/Delta_potential
http://quantummechanics.ucsd.edu/ph130a/130_notes/node154.html

Next you solve the same problem, but with the additional boundary condition that the wave function must vanish at the boundaries of the infinite potential well: $\psi(a)=\psi(-a)=0$. This additional constraint makes the energy spectrum discrete. Finally, compare the energy spectrum to that of the normal infinite potential well.