Hamiltonians with position-dependent mass, deformations and supersymmetry

2005/12/06 by C. Quesne, Quesne, C., Bijan Bagchi +5
Chemistry · #FOS: Physical sciences #Inorganic Fluorides and Related Compounds #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.quant-ph/0512046

openalex publication_date 2005/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new method for generating exactly solvable Schrödinger equations with a position-dependent mass is proposed. It is based on a relation with some deformed Schrödinger equations, which can be dealt with by using a supersymmetric quantum mechanical approach combined with a deformed shape-invariance condition. The solvability of the latter is shown to impose the form of both the deformed superpotential and the position-dependent mass. The conditions for the existence of bound states are determined. A lot of examples are provided and the corresponding bound-state spectrum and wavefunctions are reviewed.

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