Solutions of the three-dimensional radial Dirac equation from the Schrödinger equation with one-dimensional Morse potential

2017/04/30 by M. G. Garcia, Garcia, M. G., Antonio S. de Castro +5 · 1 citation
Physics and Astronomy · #Advanced Fiber Laser Technologies #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1705.00310

openalex publication_date 2017/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

New exact analytical bound-state solutions of the radial Dirac equation in 3+1 dimensions for two sets of couplings and radial potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of equations that can be transformed into polynomial equations. Several analytical results found in the literature, including the Dirac oscillator, are obtained as particular cases of this unified approach.

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