When I was learning translational symmetry I saw that for translation invariance, i.e [T,H]=0the momentum P needs to be conserved [P,H]=0. This momentum is actually the generator of small translations defined as T:x→x+ε. Now, I was solving some problems and I met one which is interesting. I am given a potential V(x)=Asin(2πx/ε) (where A is a constant)That potential is actually invariant under the translation defined above. In that problem they say that consequently the "momentum is not conserved". Can anybody tell me why? I tried to understand it by saying that, if I can show that the Hamiltonian is not conserved hence the momentum is not. But it looks that I don't have enough information about H.