Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419293 | Journal of Mathematical Analysis and Applications | 2012 | 8 Pages |
Abstract
We consider two types of Schrödinger operators H(t)=âd2/dx2+q(x)+tcosx and H(t)=âd2/dx2+q(x)+Acos(tx) defined on L2(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 λ1(t) and λ2(t) the lowest eigenvalue and the second one, respectively. The purpose of this paper is to study the asymptotics of the gap Î(t)=λ2(t)âλ1(t) in the limit as tââ.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Duo-Yuan Chen, Min-Jei Huang,