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The Harper equation: Monodromization without quasiclassics. (Russian) Zbl 0849.34066

The Harper equation has the form \[ {\psi (x + h) + \psi (x - h) \over 2} + \cos x \psi (x) = E \psi (x).\tag{1} \] In previous papers the authors have investigated the spectrum of the equation by a monodromization method under the condition (2) \(h \ll 1\) (quasiclassical case). In this paper the authors omit condition (2).

MSC:

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
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