Struggling with 3-D Hamiltonian for Variational Principle Integration?

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SUMMARY

The discussion revolves around the challenges faced in formulating a 3-D Hamiltonian for the Variational Principle Integration in a specific homework problem. The user initially struggled with the correct representation of the Hamiltonian while performing integrals for part (b) of the assignment. After seeking assistance, the user resolved their confusion and successfully completed the task.

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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.
 

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