# Mathieu Function Problem [Need Help]

1. Jun 22, 2008

### MipT.Cervix

There is a mathematical problem in quantum mechanics:
$$$\left\{\begin{array}{ll} u''+(\varepsilon-2\alpha\cos\phi)u=0&\alpha\gg 1\\u(\phi)e^{i\beta\phi}\quad -2\pi\textrm{-periodic function}\end{array}\right.$$$
I've found a lot of articles like this one describing $$\alpha\ll 1$$ case.
Do you have any ideas how to get (approximately!) the dependence $$\varepsilon(\alpha,\beta)$$ for the ground state(minimal $$\varepsilon$$)? Or mb you can give me some links to such articles or books?
Thx for your attention.

Last edited: Jun 22, 2008