How to Solve Schroedinger Problems by Approximating the Potential Function

Journal Article · Thu Sep 30 04:00:00 EDT 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3498561· OSTI ID:21428615

Ledoux, Veerle ^[1]; Van Daele, Marnix ^[1]

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1. Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Krijgslaan 281-S9, B-9000 Gent (Belgium)

We give a survey over the efforts in the direction of solving the Schroedinger equation by using piecewise approximations of the potential function. Two types of approximating potentials have been considered in the literature, that is piecewise constant and piecewise linear functions. For polynomials of higher degree the approximating problem is not so easy to integrate analytically. This obstacle can be circumvented by using a perturbative approach to construct the solution of the approximating problem, leading to the so-called piecewise perturbation methods (PPM). We discuss the construction of a PPM in its most convenient form for applications and show that different PPM versions (CPM,LPM) are in fact equivalent.

• OSTI ID: 21428615
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1281; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
APPROXIMATIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONAL ANALYSIS
FUNCTIONS
MATHEMATICAL SOLUTIONS
MATHEMATICS
MATRICES
NUMERICAL ANALYSIS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
POLYNOMIALS
POTENTIALS
SCHROEDINGER EQUATION
WAVE EQUATIONS