- #1
Wishe Deom
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Homework Statement
Consider a particle of mass m moving in a 3D-anisotropic oscillator potential:
[tex]V(\vec{r}) = \frac{1}{2}m(\omega^{2}_{x}x^{2}+\omega^{2}_{y}y^{2}+\omega^{2}_{z}z^{2})[/tex]. (a) Frind the stationary states for this potential and their respective energies.
Homework Equations
Time-Independent Schroedinger Equation in 3 dimensions is [tex]\frac{\bar{h}^{2}}{2m}\nabla^{2}\psi+V\psi=E\psi[/tex]
The Attempt at a Solution
I first tried to find solutions to the TISE in the form of [tex]\psi=X(x)Y(y)Z(z)[/tex], taking all the partial derivatives, dividing through by XYZ, and arranging one side to be a function of x, and the other to be a function of y and z, equaling a constant of separation A.
However, when solving for X(x), I have an equation of the form [tex]\frac{\partial^{2}X}{\partial x^2} = (C + x^2}X[/tex]. I have no idea how to solve this for X. Am I apporaching this problem in the correct way?