Solving 2D Oscillator: Hamiltonian Op & Eigenvalue Analysis

[anjwolf2000]

I would be eternally grateful if I could get some help. The question is: Write down the Haniltonian operator for the 2D harmonic oscillator with the potential V(x,y)=1/2(x^2+y^2).

By using the separation of variables and theform of the eigenvalue for the 1D harmoinc oscillator, find the energy eigenvalues for the 2D oscillator.

 

[malawi_glenn]

show your attempt to solution!

What is your ansatz for eigenfunction with separation of variables?