Struggling with 3-D Hamiltonian for Variational Principle Integration?

[Airsteve0]

Homework Statement

The problem statement is a bit length so I have attached a picture of the problem instead. The issue I am having pertains to part (b).

Homework Equations

The Attempt at a Solution

The main issue I am having is with what my Hamiltonian should look like when I do the integrals for part (b). Since the problem is in 3-D I'm just second guessing everything I write down. Any assistance is greatly appreciated.

 

[Airsteve0]

nvm got it