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Quesne, C. and Tkachuk, V.M. (2007) Generalized Deformed Commutation Relations with Nonzero Minimal Uncertainties in Position and/or Momentum and Applications to Quantum Mechanic. SIGMA, 3, 016.

has been cited by the following article:

• TITLE: Analytical Solutions of the 1D Dirac Equation Using the Tridiagonal Representation Approach

  AUTHORS: Ibsal A. Assi, Hocine Bahlouli

  KEYWORDS: Dirac Equation, Tridiagonal Representation, Three-Term Recursion Relation, Orthogonal Polynomials, Energy Spectrum, Isospectral Potentials, Spin-Symmetric Coupling, Pseudo-Spin-Symmetric Coupling, Graphene

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.10, October 31, 2017

  ABSTRACT: 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.