arXiv:nucl-th/0309038 · Computational and Group-Theoretical Methods in Nuclear Physics

SHAPE-INVARIANCE AND EXACTLY SOLVABLE PROBLEMS IN QUANTUM MECHANICS

A. B. Balantekin

Published Feb 1, 2004• 1 citation

Abstract

Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent two-level systems are examined. These generalize the Jaynes-Cummings Hamiltonian. Coherent states associated with shape-invariant systems are discussed. For the case of quantum harmonic oscillator the decomposition of identity for these coherent states is given. This decomposition of identity utilizes Ramanujan's integral extension of the beta function.

DOI: 10.1142/9789812703026_0018

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