The functional structure of the monodromy matrix for Harper’s equation. (English) Zbl 0816.34058

Buslaev, Vladimir; Fedotov, Alexander

Demuth, Michael (ed.) et al., Mathematical results in quantum mechanics: International conference in Blossin (Germany), May 17-21, 1993. Basel: Birkhäuser Verlag. Oper. Theory, Adv. Appl. 70, 321-342 (1994).

The authors study the functional structure of the monodromy matrix for Harper’s equation on the base of the author’s former work [Reports of Mittag-Leffler Institute 11 (1993)]. This equation appeared as a model for Bloch electron in a weak constant magnetic field. The monodromy matrix corresponding to the basis solutions of Harper’s equation is constructed and the relations between the monodromy matrix coefficients are found.
For the entire collection see [Zbl 0791.00039].

Reviewer: Jiang Furu (Shanghai)

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:

monodromy matrix; Harper’s equation; Bloch electron in a weak constant magnetic field