- #1
JohnSimpson
- 89
- 0
I'm solving the 2D harmonic oscillator, numerically.
<br /> -\frac{1}{2}\left(<br /> u_{xx} + u_{yy}\right) + \frac{1}{2}(x^2+y^2)u = Eu<br />
The solutions my solver spits out for say, the |01> state, are linear combinations of the form
<br /> |u\rangle = \alpha_1 |01\rangle + \alpha_2 |10\rangle<br />
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
<br /> -\frac{1}{2}\left(<br /> u_{xx} + u_{yy}\right) + \frac{1}{2}(x^2+y^2)u = Eu<br />
The solutions my solver spits out for say, the |01> state, are linear combinations of the form
<br /> |u\rangle = \alpha_1 |01\rangle + \alpha_2 |10\rangle<br />
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
