Momentum Eigenstate with a non-zero potential

[QFT25]

Homework Statement

Prove that if a particle starts in a momentum eigenstate it will remain forever in a eigenstate given the potential c*y where c is a constant and y is a spatial variable.

Homework Equations

(h/i)d/dx is the momentum operator and a momentum eigenstate when put in the momentum operator gives an eigenvalue times the momentum eigenstate.

The Attempt at a Solution

If p commutes with H then a eigenstate of H is an eigenstate of p always. My problem is that p does not commute with H and I always thought that you can only have momentum eigenstates for systems with with zero potential. So I'm at a loss where to begin because if I workout the Heisenberg equations I get dp/dt where p is the operator in the Heisenberg picture to be none zero. Any help will be much appreciated.[/B]

 

[QFT25]

Can an momentum eigenstate have a eigenvalue which is time dependent.