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EXACT NUMERICAL SOLUTION OF SCHRÖDINGER'S EQUATION FOR A PARTICLE IN AN INTERACTION POTENTIAL OF GENERAL SHAPE

Forschungszentrum Karlsruhe, Institut für Materialforschung I, P.O. Box 3460, 76221 Karlsruhe, Germany

University of Patras, School of Engineering, Engineering Science Department, 26500 Patras, Greece

Corresponding author.

Forschungszentrum Karlsruhe, Hauptabteilung Informations- und Kommunikationstechnik, P.O. Box 3640, 76221 Karlsruhe, Germany

University of Patras, School of Engineering, Engineering Science Department, 26500 Patras, Greece

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S. BASKOUTAS

University of Patras, School of Engineering, Materials Science Department, 26500 Patras, Greece

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https://doi.org/10.1142/S0217979202014802Cited by:45 (Source: Crossref)

Abstract

A method is proposed for the quantum-mechanical determination of the eigenstates and eigenvalues of a particle (e.g. an electron) in a potential of general shape. For such systems the method allows one to calculate the exact solutions of the stationary Schrödinger equation. For the application of this method any well-known reference system is needed. A transition from the stationary reference system to the stationary system under investigation is performed by means of the time-dependent Schrödinger equation. The results are compared with various standard methods; alternative numerical methods will be discussed critically.

Keywords:

PACS: 73.22.-f, 03.65.Ge, 03.67.Lx, 26.60.+c