STATIONARY-PHASE METHOD IN INFINITE DIMENSIONS BY FINITE-DIMENSIONAL APPROXIMATIONS - APPLICATIONS TO THE SCHRODINGER-EQUATION

被引：16

作者：

ALBEVERIO, S

DEMONVELBERTHIER, AB

BRZEZNIAK, Z

机构：

[1] UNIV BIELEFELD,BIBOS RES CTR,D-33615 BIELEFELD,GERMANY

[2] UNIV PARIS 07,PHYS MATH & GEOMETRIE LAB EP0004,F-75251 PARIS 05,FRANCE

来源：

POTENTIAL ANALYSIS | 1995年 / 4卷 / 05期

关键词：

INFINITE DIMENSIONAL OSCILLATORY INTEGRALS; STATIONARY PHASE METHOD; FREDHOLM DETERMINANT; SEMICLASSICAL ASYMPTOTIC EXPANSION; SCHRODINGER EQUATION; CLASSICAL MECHANICS; CRITICAL POINTS; DEGENERATE AND NONDEGENERATE; CATASTROPHE THEORY;

D O I：

10.1007/BF01048065

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop an approach by finite dimensional approximations for the study of infinite dimensional oscillatory integrals and the relative method of stationary phase. We provide detailed asymptotic expansions in the nondegenerate as well as in the degenerate case. We also give applications to the derivation of detailed asymptotic expansions in Planck's constant for the Schrodinger equation.

引用

页码：469 / 502

页数：34

共 79 条

[1] FINITE-DIMENSIONAL APPROXIMATION APPROACH TO OSCILLATORY INTEGRALS AND STATIONARY PHASE IN INFINITE DIMENSIONS [J].