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Quantum Mechanics: Time Independent Perturbation

I have a negative potential, -V in the center of an inifinite square well. The well extends from -a to +a and the unperturbed wave functions 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

Calculate the first-order time independent perturbation correction to the energy of the ground state.

Calculate the first order corrections to the ground state wave function for the case of b <<< a.

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