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For a harmonic oscillator in 3D the energy level becomes E_{n}= hw(n+3/2) (Note: h = h_bar and n = n_{x}+n_{y}+n_{z}) If I then want the 1st excited state it could be (1,0,0), (0,1,0) and (0,0,1) for x, y and z.

But what happens if for example y has a different value from the beginning? Like this: V(x,y,z) = 1/2mw^{2}(x^{2}+4y^{2}+z^{2}) and for this decide the energy level AND degeneracy for the 1st excited state. I can only find simple examples when x, y and z are equal and 1.

Best regards

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# I Harmonic Oscillator in 3D, different values on x, y and z

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