Splitting formulas for the higher and lower energy levels of the one-dimensional Schrodinger operator

被引：5

作者：

Albeverio, S ^{[1
]}

Dobrokhotov, SY

Semenov, ES

机构：

[1] Univ Bonn, Inst Angew Math, D-5300 Bonn, Germany

[2] Russian Acad Sci, Inst Problems Mech, Moscow, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2004年 / 138卷 / 01期

关键词：

tunneling; Schrodinger equation; splitting of energy levels; double-well potential; asymptotic expression; eigenvalues;

D O I：

10.1023/B:TAMP.0000010637.91646.c2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We compare the asymptotic formulas for splitting higher and lower energy levels for the one-dimensional Schrodinger operator with the double-well potential. We. establish that the splitting value for the lower energy level is proportional to that calculated for the higher levels with the factor roote/pi. An analogous result is found for the width of bands in the periodic case.

引用

页码：98 / 106

页数：9

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