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A GENERAL SCHEME FOR THE EFFECTIVE-MASS SCHRÖDINGER EQUATION AND THE GENERATION OF THE ASSOCIATED POTENTIALS

Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India

Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium

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, and

R. ROYCHOUDHURY

Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700035, India

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https://doi.org/10.1142/S0217732304016123Cited by:113 (Source: Crossref)

Abstract

A systematic procedure to study one-dimensional Schrödinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting situation in that, in the presence of a mass background, formation of bound states is signalled. We also discuss coordinate-transformed, constant-mass Schrödinger equation, its matching with the PDEM form and the consequent decoupling of the ambiguity parameters. This provides a unified approach to many exact results known in the literature, as well as to a lot of new ones.

Keywords:

PACS: 03.65.Ca, 03.65.Ge, 02.30.Hq

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