From the generalized Morse potential to a unified treatment of the\n D-dimensional singular harmonic oscillator and singular Coulomb potentials

2016/05/01 by Pedro H. F. Nogueira, Nogueira, Pedro H. F., Antonio S. de Castro +1
Earth and Planetary Sciences · Physics and Astronomy · #FOS: Physical sciences #High-pressure geophysics and materials #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.1605.00280

openalex publication_date 2016/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Bound-state solutions of the singular harmonic oscillator and singular\nCoulomb potentials in arbitrary dimensions are generated in a simple way from\nthe solutions of the one-dimensional generalized Morse potential. The\nnonsingular harmonic oscillator and nonsingular Coulomb potentials in arbitrary\ndimensions with their additional accidental degeneracies are obtained as\nparticular cases. Added bonuses from these mappings are the straightforward\ndetermination of the critical attractive singular potential, the proper\nboundary condition on the radial eigenfunction at the origin and the\ninexistence of bound states in a pure inversely quadratic potential.\n

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