Iterative solutions to the Dirac equation

Abstract

We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a screened-Coulomb potential and for a Coulomb plus linear potential with linear scalar confinement, the method is used to obtain accurate approximate solutions for both eigenvalues and wave functions.

18 pages

References in corpus (13)

• Asymptotic iteration method for eigenvalue problems
• Construction of exact solutions to eigenvalue problems by the asymptotic iteration method
• Energy spectrum of the relativistic Dirac-Morse problem
• The Woods-Saxon Potential in the Dirac Equation
• Relativistic shape invariant potentials
• The Relativistic Levinson Theorem in Two Dimensions
• Solution of the relativistic Dirac-Morse problem
• Levinson's Theorem for Dirac Equation
• Spectral Comparison Theorem for the Dirac Equation
• Levinson theorem for Dirac particles in two dimensions
• The Strong Levinson Theorem for the Dirac Equation
• A simple Dirac wave function for a Coulomb potential with linear confinement
• Multiverse cosmological models

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• The Asymptotic Iteration Method Revisited
• Supersymmetric analysis for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions
• Solution of spin-boson systems in one and two-dimensional geometry via the asymptotic iteration method
• New exact solution of Dirac-Coulomb equation with exact boundary condition
• Quarkonium and hydrogen spectra with spin dependent relativistic wave equation
• Quasinormal frequencies of a two-dimensional asymptotically anti-de Sitter black hole of the dilaton gravity theory
• Solution of the Bosonic and Algebraic Hamiltonians by using AIM
• AIMpy: A Python code to solve Schrödinger-like equations with the asymptotic iteration method
• Solvable Systems of Linear Differential Equations
• Historical pseudo simplified solution of the Dirac-Coulomb equation
• hp-Cloud Approximation Of The Dirac Eigenvalue Problem: The Way Of Stability