ALGEBRAIC DESCRIPTION OF SHAPE INVARIANCE REVISITED

Satoshi Ohya

Abstract


We revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical space, the Kepler problem in hyperbolic space, and the Rosen-Morse potential problem. Following the prescription given by Gangopadhyaya et al., we introduce new nonlinear algebraic systems and solve the bound-state problems by means of representation theory.

Keywords


exactly solvable models; shape invariance; representation theory

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague