Construction of the asymptotics of the solutions of the one-dimensional Schrodinger equation with rapidly oscillating potential

被引：13

作者：

Nesterov, P. N. ^{[1
]}

机构：

[1] PG Deminov Yaroslavl State Univ, Yaroslavl, Russia

来源：

MATHEMATICAL NOTES | 2006年 / 80卷 / 1-2期

关键词：

Schrodinger equation; averaging method; oscillating potential; Levinson's theorem;

D O I：

10.1007/s11006-006-0132-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain asymptotic formulas for the solutions of the one-dimensional Schrodinger equation -y" + q(x)y = 0 with oscillating potential q(x) = x(beta)P(x(1+alpha),) + cx(-2) as x -> +infinity. The real parameters alpha and beta satisfy the inequalities beta - alpha > -1, 2 alpha - beta > 0 and c is an arbitrary real constant. The real function P(x) is either periodic with period T, or a trigonometric polynomial. To construct the asymptotics, we apply the ideas of the averaging method and use Levinson's fundamental theorem.

引用

页码：233 / 243

页数：11