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Consider a harmonic oscillator of mass m undergoing harmonic motion in two dimensions x and y. The potential energy is given by

V(x,y) = (1/2)kxx2 + (1/2)kyy2.

(a) Write down the expression for the Hamiltonian operator for such a system.

(b) What is the general expression for the allowable energy levels of the two-dimensional harmonic oscillator?

(c) What is the energy of the ground state (the lowest energy state)?

Hint: The Hamiltonian operator can be written as a sum of operators.

Now I'm a bit lost on how to write the expression for the Hamiltonian.

Is the Hamiltonian simply H = - h2/2m d2/dx2 + V(x,y) [where V(x,y) is given above]?

Then with that Hamiltonian, solving the Schrodinger eqn is pretty straightforward to get H*psi = E*psi, now I'm a bit lost here as well to solve for the general expression for the allowable energy levels?

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# Harmonic Oscillator

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