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Mathieu Function Problem [Need Help]

  1. Jun 22, 2008 #1
    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 [tex]$\alpha\ll 1$[/tex] case.
    Do you have any ideas how to get (approximately!) the dependence [tex]$\varepsilon(\alpha,\beta)$[/tex] for the ground state(minimal [tex]$\varepsilon$[/tex])? Or mb you can give me some links to such articles or books?
    Thx for your attention.
    Last edited: Jun 22, 2008
  2. jcsd
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