SHAPE-INVARIANCE AND EXACTLY SOLVABLE PROBLEMS IN QUANTUM MECHANICS

DOI10.1142/9789812703026_0018zbMATH Open1198.81187arXivnucl-th/0309038OpenAlexW2029681416MaRDI QIDQ4823098

A. B. Balantekin

Publication date: 26 October 2004

Published in: Computational and Group-Theoretical Methods in Nuclear Physics (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/nucl-th/0309038

Mathematics Subject Classification ID

Nuclear physics (81V35) Exactly and quasi-solvable systems arising in quantum theory (81U15)

Related Items (2)

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