Solution of the relativistic Dirac Hulthén problem
Abstract
The oneparticle threedimensional Dirac equation with spherical symmetry is solved for the Hulthén potential. The swave relativistic energy spectrum and twocomponent spinor wavefunctions are obtained analytically. Conforming to the standard feature of the relativistic problem, the solution space splits into two distinct subspaces depending on the sign of a fundamental parameter in the problem. Unique and interesting properties of the energy spectrum are pointed out and illustrated graphically for several values of the physical parameters. The square integrable twocomponent wavefunctions are written in terms of the Jacobi polynomials. The nonrelativistic limit reproduces the wellknown nonrelativistic energy spectrum and results in Schrödinger equation with a 'generalized' threeparameter Hulthén potential, which is the sum of the original Hulthén potential and its square.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 June 2004
 DOI:
 10.1088/03054470/37/22/007
 arXiv:
 arXiv:hepth/0405022
 Bibcode:
 2004JPhA...37.5805A
 Keywords:

 dirac equationhulthén potentialenergy spectrum;
 High Energy Physics  Theory
 EPrint:
 13 pages, 3 color figures