- #1

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## Homework Statement

## Homework Equations

## 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

Any ideas, or are my problems due to a mistake in working?