One continuous parameter family of Dirac Lorentz scalar potentials associated with exceptional orthogonal polynomials

2023/09/22 by Suman Banerjee, Rajesh Kumar Yadav, Banerjee, Suman +1
Mathematics · Physics and Astronomy · #81Q05 #81Q60 #Advanced Mathematical Physics Problems #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2309.12965

openalex publication_date 2023/09/22 · openalex created_date 2023/09/26 · openalex updated_date 2026/07/28

Abstract

We extend our recent works [ Int. J. Mod. Phys. A 38 (2023) 2350069-1] and obtain one parameter (λ) family of rationally extended Dirac Lorentz scalar potentials with their explicit solutions in terms of X_m exceptional orthogonal polynomials. We further show that as the parameter λ→ 0 or -1, we get the corresponding rationally extended Pursey and the rationally extended Abraham-Moses type of scalar potentials respectively, which have one bound state less than the starting scalar potentials.

Related

• One parameter family of rationally extended isospectral potentials
• Rationally extended shape invariant potentials in arbitrary D-dimensions associated with exceptional X_m polynomials
• Spin and Pseudo-Spin Symmetries in Radial Dirac Equation and Exceptional\n Hermite Polynomials
• The linear potential and the Dirac equation
• Algebraic derivation of spectrum of the Dirac Hamiltonian for arbitrary combination of Lorentz-scalar and Lorentz-vector Coulomb potentials