## 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

### Keywords:

Harper equation; spectrum; monodromization