Solution of the spin and pseudo-spin symmetric Dirac equation in 1+1 space-time using the tridiagonal representation approach

Abstract

The aim of this work is to find exact solutions of the Dirac equation in 1+1 space-time beyond the already known class. We consider exact spin (and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus (and minus) the vector potential. We also include pseudo-scalar potentials in the interaction. The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis, which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric. This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.

23 pages, 2 tables

References in corpus (7)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Magnetic confinement of massless Dirac fermions in graphene
• Solution of the nonrelativistic wave equation in the tridiagonal representation approach
• Exact solution of the Klein Gordon equation in the presence of a minimal length
• Orthogonal polynomials derived from the tridiagonal representation approach
• Generalizing spin and pseudospin symmetries for relativistic spin 1/2 fermions

Cited by in corpus (2)

• Open problem in orthogonal polynomials
• Exact solvability of two new 3D and 1D nonrelativistic potentials within the TRA framework