Semi-spectral Chebyshev method in quantum mechanics

Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics, astrophysics, quantum chemistry, etc. In recent years, however, a...

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Bibliographic Details
Published inAnnals of physics Vol. 322; no. 6; pp. 1373 - 1419
Main Author Deloff, A.
Format Journal Article
LanguageEnglish
Published New York Elsevier Inc 01.06.2007
Elsevier BV
Subjects
ASTROPHYSICS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONVERGENCE
COORDINATES
FINITE ELEMENT METHOD
LIPPMANN-SCHWINGER EQUATION
Physics
QUANTUM MECHANICS
Quantum theory
SCHROEDINGER EQUATION
Schrödinger equation
Semi-spectral method
TWO-BODY PROBLEM
31.15
02.70.Hm
c
03.65.Ge
Semi-spectral method
03.67.Lx
Lippmann–Schwinger equation
02.70
Schrödinger equation
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Summary:Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics, astrophysics, quantum chemistry, etc. In recent years, however, an alternative technique based on the semi-spectral methods has focused considerable attention. The purpose of this work is first to provide the necessary tools and subsequently examine the efficiency of this method in quantum mechanical applications. Restricting our interest to time-independent two-body problems, we obtained the continuous and discrete spectrum solutions of the underlying Schrödinger or Lippmann–Schwinger equations in both, the coordinate and momentum space. In all of the numerically studied examples we had no difficulty in achieving the machine accuracy and the semi-spectral method showed exponential convergence combined with excellent numerical stability.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2006.07.004