2017/01/29 by I. A. Assi, Ibsal. Assi, Assi, Ibsal. +3
Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1702.00051
arxiv created 2017/01/29 · openalex publication_date 2017/01/29 · arxiv updated 2017/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper aims at extending our previous work on the solution of the one-dimensional Dirac equation using the Tridiagonal Representation Approach (TRA). In the approach, we expand the spinor wavefunction in terms of suitable square integrable basis functions that support a tridiagonal matrix representation of the wave operator. This will transform the problem from solving a system of coupled first order differential equations to solving an algebraic three-term recursion relation for the expansion coefficients of the wavefunction. In some cases, solutions to this recursion relation can be related to well-known classes of orthogonal polynomials whereas in other situations solutions represent new class of polynomials. In this work, we will discuss various solvable potentials that obey the tridiagonal representation requirement with special emphasis on simple cases with spin-symmetric and pseudospin-symmetric potential couplings. We conclude by mentioning some potential applications in graphene.