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Adiabatic perturbation theory. Semiclassical limit of the reflection coefficient on a potential barrier

Abstract

Using methods of Adiabatic Perturbation Theory, the asymptotic behaviour in the semiclassical limit of the reflection coefficient for one dimensional collisions in quantum mechanics is studied rigorously. In this limit we give a recursive method for an exact calculation to all orders. In contrast to other methods (which fail), our method still works when the energy is near or equal to the top of the potential. First we derive the coefficient for a specific potential. Then we give the coefficient to first three orders for an arbitrary potential depending only on the potential`s behaviour around its maximum. We point out that each term needs to be analyzed to ``all orders``. (orig.)
Authors:
Firica, G [1] 
  1. Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
Publication Date:
Oct 01, 1993
Product Type:
Technical Report
Report Number:
DESY-93-142
Reference Number:
SCA: 661100; PA: DEN-94:0F7173; EDB-94:084760; ERA-19:019923; NTS-95:004777; SN: 94001207844
Resource Relation:
Other Information: PBD: Oct 1993
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM MECHANICS; POTENTIAL SCATTERING; PERTURBATION THEORY; POTENTIALS; RECURSION RELATIONS; REFLECTION; SEMICLASSICAL APPROXIMATION; ADIABATIC APPROXIMATION; ONE-DIMENSIONAL CALCULATIONS; S MATRIX; HAMILTONIANS; WAVE PROPAGATION; SCHROEDINGER EQUATION; ASYMPTOTIC SOLUTIONS; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10153339
Research Organizations:
Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 0418-9833; Other: ON: DE94768984; TRN: DE94F7173
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
DEN
Size:
36 p.
Announcement Date:
Jul 06, 2005

Citation Formats

Firica, G. Adiabatic perturbation theory. Semiclassical limit of the reflection coefficient on a potential barrier. Germany: N. p., 1993. Web.
Firica, G. Adiabatic perturbation theory. Semiclassical limit of the reflection coefficient on a potential barrier. Germany.
Firica, G. 1993. "Adiabatic perturbation theory. Semiclassical limit of the reflection coefficient on a potential barrier." Germany.
@misc{etde_10153339,
title = {Adiabatic perturbation theory. Semiclassical limit of the reflection coefficient on a potential barrier}
author = {Firica, G}
abstractNote = {Using methods of Adiabatic Perturbation Theory, the asymptotic behaviour in the semiclassical limit of the reflection coefficient for one dimensional collisions in quantum mechanics is studied rigorously. In this limit we give a recursive method for an exact calculation to all orders. In contrast to other methods (which fail), our method still works when the energy is near or equal to the top of the potential. First we derive the coefficient for a specific potential. Then we give the coefficient to first three orders for an arbitrary potential depending only on the potential`s behaviour around its maximum. We point out that each term needs to be analyzed to ``all orders``. (orig.)}
place = {Germany}
year = {1993}
month = {Oct}
}