1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution So far I have a solution for a) as For b) I formulate the equation as and so far for c) I have My main idea at the moment is that as the Lagrangian was not time dependent, the Hamiltonian will not be. Following on maybe I can say that when separating variables T is constant so I can separate it so but this is as far as I could get, as I couldn't think of how to separate them. Any ideas, or are my problems due to a mistake in working?