Solution of the Dirac Equation with Special Hulthén Potentials

¹School of Physics, Peking University, Beijing 100871 ²Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080 ³Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000 ⁴Department of Physics, Anhui University, Hefei 230039

Published Date: April 30, 2003

Abstract

The Dirac equation for the special case of a spinor in the relativistic potential with the even and odd components related by a constraint is solved exactly when the even component is chosen to be the Hulthén potential. The corresponding radial wavefunctions for two-component spinor are obtained in terms of the hypergeometric function, and the energy spectrum of the bound states is obtained as a solution to a given equation by boundary constraints, in which the nonrelativistic limit reproduces the usual Hulthén potential.