First order perturbation theory problem

[Bowenwww]

Ok so I have a classic particle in a box problem. If a particle in a box, the states of which are given by: ψ = (√2/L) * sin(nπx/L) where n=1,2,3...

is perturbed by a potential v(x) = γx , how do I calculate the energy shift of the ground state in first order perturbation

I'm guessing that the energy shift is given by the expectation value of this perturbation but apart from that I'm stumped.

Thanks in advance guys

 

[qbert]

hint: you should calculate the expectation of the perturbation with respect to which state?