Solution of the Dirac Equation and the Solvable Potentials in the Schrodinger Equation

摘要

The point canonical transformation in non-relativistic quantum mechanics is applied as an algebraic method to obtain the solutions of the Dirac equation with spherical symmetry electromagnetic potentials. We show that some of the solvable potentials in the non-relativistic quantum mechanics can be related to the Dirac equation. The spinor wave functions for some of the obtained gauge field potentials are given in terms of special functions such as Jacobi, Generalized Laguerre and Hermit polynomials. The relativistic bound states spectrum for each cases are also obtained in terms of the bound states spectrum of the solvable potentials.