1. The problem statement, all variables and given/known data Are the momentum eigenfunctions also eigenfunctions of e free particle energy. Operator? Are momentum eigenfunctions also eigenfunctions of the harmonic oscillator energy operator? An misplayed system evolves with time according to the shrodinger equation with potential v. The wave function depends on time. Does the expectation value of energy depend on time? 2. Relevant equations 3. The attempt at a solution I think not necessarily. Looking at the commutator it looks like this would only work if the potential was a constant. I guess this is a no judging by the form of the eigenfunctions of the two. Does this depend on the initial conditions? It snot clear wether or not this is a stationary state?