Numerical 2D Harmonic Oscillator

I'm solving the 2D harmonic oscillator, numerically.

u_{xx} + u_{yy}\right) + \frac{1}{2}(x^2+y^2)u = Eu

The solutions my solver spits out for say, the |01> state, are linear combinations of the form

|u\rangle = \alpha_1 |01\rangle + \alpha_2 |10\rangle

which is obviously a perfectly fine solution which has the correct eigenvalue. But I'd like for my solver to somehow be "smart" enough to generate the typically defined pure gauss-hermite solutions, automatically. Is there any way to force this?

I decided just to break the degeneracy by choosing different frequencies in the different directions. Nevermind!

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