Asymptotic Solutions of the One-dimensional Schrödinger Equation
( Translations of Mathematical Monographs )
Publication series ： Translations of Mathematical Monographs
Author： Sergei Yu. Slavyanov
Publisher： American Mathematical Society
Publication year： 2018
E-ISBN: 9781470445669
P-ISBN(Paperback): 9780821805367
Subject： O175 differential equations, integral equations
Keyword： 数学
Language： ENG
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Asymptotic Solutions of the One-dimensional Schrödinger Equation
Description
This book is devoted to asymptotic analysis of solutions of second order ordinary differential equations with a small parameter. The main emphasis is on various constructive schemes of obtaining asymptotic solutions, their advantages and drawbacks, and specific computations. The author gives a complete overview of the state of the theory and also concentrates on some lesser known aspects and problems, in particular the problems in which exponentially small terms should be taken into account or the analysis of equations with close transition points. Such applications as the derivation of the formulas for the quasiclassical quantizations, spectrum splitting in a symmetrical potential, etc., are considered.
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