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

Buslaev, V. S.; Fedotov, A. A.

Algebra Anal. 8, No. 2, 65-97 (1996).

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).

Reviewer: L.A.Sakhnovich (Odessa)

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