An Algebraic Construction of Generalized Coherent States for Shape-Invariant Potentials

Abstract

Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary to establish a connection between classical and quantum formulations of a given system (continuity of labeling, resolution of unity, temporal stability, and action identity); b) reproduce results already known for shape-invariant systems, like harmonic oscillator, double anharmonic, Poschl-Teller and self-similar potentials and; c) point to a formalism that provides an unified description of the different kind of coherent states for quantum systems.

arXiv comment14 pages of REVTEX

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• Ladder operators and squeezed coherent states of a 3-dimensional generalized isotonic nonlinear oscillator
• Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties