- #1
JordanGo
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Homework Statement
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.
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 ψx, ψy or ψz.
Can someone help me?