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Infinite potential well with Delta function inside!

  1. Jan 20, 2014 #1
    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 existance 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:smile:
     
  2. jcsd
  3. Jan 20, 2014 #2

    hilbert2

    User Avatar
    Science Advisor
    Gold Member

    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.
     
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