(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 3D harmonic oscillator has the following potential:

[itex] V(x,y,z) = \frac{1}{2}m( \varpi_{x}^2x^2 + \varpi_{y}^2y^2 + \varpi_{z}^2z^2) [/itex]

Find the energy eigenstates and energy eigenvalues for this system.

3. The attempt at a solution

I found the energy eigenvalue to be:

[itex] E = E_{x} + E_{y} + E_{z} [/itex]

[itex] E = \hbar((n_{x}+\frac{1}{2})\varpi_{x} + (n_{y}+\frac{1}{2})\varpi_{y} + (n_{z}+\frac{1}{2})\varpi_{z}) [/itex]

Now I know that the eigenstate is:

[itex] \Psi = \Psi_{x} \times \Psi_{y} \times \Psi_{z} [/itex]

But I don't know how to find ψ_{x}, ψ_{y}or ψ_{z}.

Can someone help me?

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# Homework Help: Eigenstate for a 3D harmonic oscillator

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