On the semiclassical approximation to the eigenvalue gap of Schrodinger operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Chen, Duo-Yuan¹  Huang, Min-Jei¹ 

[1] Natl Tsing Hua Univ, Dept Math, Hsinchu 30043, Taiwan

关键词: Schrodinger operator;    Semiclassical limit;    Eigenvalue gap;    Eigenfunction;    Even potential;    Periodic potential;   

DOI  :  10.1016/j.jmaa.2012.01.002

来源: Elsevier

【 摘 要 】

We consider two types of Schrodinger operators H(t) = -d(2)/dx(2) + q(x)+ t cosx and H(t) = -d(2)/dx(2) + q(x) + A cos(tx) defined on L-2(R), where q is an even potential that is bounded from below, A is a constant, and t > 0 is a parameter. We assume that H(t) has at least two eigenvalues below its essential spectrum: and we denote by lambda(1) (t) and lambda(2) (t) the lowest eigenvalue and the second one, respectively. The purpose of this paper is to study the asymptotics of the gap Gamma(t) = lambda(2)(t) - lambda(1)(t) in the limit as t -> infinity. (C) 2012 Elsevier Inc. All rights reserved.

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