Quantum Mechanics: Time Indep perturbation negative potential in an infinite sq well

Hi,  

This is a problem that I have got a solution for but would really like to have a second check to make sure that I have done it correctly.

  I have a negative potential, -V in the center of an inifinite square well.  The well extends from -a to +a and the unperturbed wevefunctions are:
  
   Si sub n (x) = sq root 1/a sin(n*pi*x/2*a) for n even
   Si sub n (x) = sq root 1/a cos(n*pi*x/2*a) for n odd

The perturbation extends from -b to +b and is given by:

    V sub 0 (x) = 0 for -a , or = x , -b
    V sub 0 (x) = -V for -b, or = x , or = +b
    V sub 0 (x) for =b, x, or = +a

The first part of the problem is to calculate the first-order Time independent perturbation correction to the energy of the ground state.

Then to calculate the first order corrections to the ground state wavefunction for the case of b <<< a.  

I would appreciate your help on this problem.  I have worked it over the best I can and would like a second set of calculations to check my work against and see if I am doing the work correctly.  I need a solution response within 12 to 15 hours.

Thank-you