This article is cited in 9 papers

Perturbation theory formulas for the Schrödinger equation with a nonsmooth periodic potential

Yu. E. Karpeshina

Leningrad State University

Abstract: Series from perturbation theory are constructed for the Bloch eigenvalues and eigenfunctions for the periodic Schrödinger operator in $R^3$. An extensive set of quasimomenta on which the series converge is described. It is shown that the series have asymptotic character at high energies. They are infinitely differentiable with respect to the quasimomentum, and preserve their asymptotic character under such differentiation.

UDC: 517.9

MSC: 35J10, 35B20, 35P20

Received: 09.01.1990

 English version: Mathematics of the USSR-Sbornik, 1992, 71:1, 101–123

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