Shape-invariance and Exactly Solvable Problems in Quantum Mechanics

Details Shape-invariance and Exactly Solvable Problems in Quantum Mechanics Shape-invariance and Exactly Solvable Problems in Quantum Mechanics

2003-09-15

arxiv.org/abs/nucl-th/0309038v1

Physics

Nuclear Physics

Nuclear Theory

To be published in the Proceedings of "Computational And Group Theoretical Methods In Nuclear Physics: Symposium In Honor Of J

Scientific paper

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.

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