JohnSimpson
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I'm solving the 2D harmonic oscillator, numerically.
[tex] -\frac{1}{2}\left(<br /> u_{xx} + u_{yy}\right) + \frac{1}{2}(x^2+y^2)u = Eu[/tex]
The solutions my solver spits out for say, the |01> state, are linear combinations of the form
[tex] |u\rangle = \alpha_1 |01\rangle + \alpha_2 |10\rangle[/tex]
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?
-js
[tex] -\frac{1}{2}\left(<br /> u_{xx} + u_{yy}\right) + \frac{1}{2}(x^2+y^2)u = Eu[/tex]
The solutions my solver spits out for say, the |01> state, are linear combinations of the form
[tex] |u\rangle = \alpha_1 |01\rangle + \alpha_2 |10\rangle[/tex]
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?
-js