A simple Dirac wave function for a Coulomb potential with linear confinement

Details A simple Dirac wave function for a Coulomb potential with linear confinement A simple Dirac wave function for a Coulomb potential with linear confinement

1998-12-21

arxiv.org/abs/hep-ph/9812464v2

Mod.Phys.Lett. A14 (1999) 2409

Physics

High Energy Physics

High Energy Physics - Phenomenology

Misprints (mostly of sign) corrected in equations (8), (9), (13), (14), (18), and (21). No change in results or discussion

Scientific paper

10.1142/S0217732399002492

A simple analytical solution is found to the Dirac equation for the combination of a Coulomb potential with a linear confining potential. An appropriate linear combination of Lorentz scalar and vector linear potentials, with the scalar part dominating, can be chosen to give a simple Dirac wave function. The binding energy depends only on the Coulomb strength, and is not affected by the linear potential. The method works for the ground state, or for the lowest state with $l=j-{1/2}$, for any $j$.

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