Exact solutions to relativistic singular fractional power potentials

Abstract

We present (exact) solutions of the Dirac equation with equally mixed interactions for a single fermion bounded by the family of fractional power singular potentials. Closed-form expressions as well as numerical values for the energies were obtained. The wave functions and the allowed values of the potential parameters for the first two members of the family are obtained in terms of a set of algebraic equations. The non relativistic limit is also discussed and using the Hellmann-Feynmann theorem, some useful expectation values are obtained.

15 Pages, 16 Figures, 2 Tables. In press JPA

References in corpus (4)

• Unified derivation of exact solutions for a class of quasi-exactly solvable models
• Spin and Pseudospin symmetries in the Dirac equation with central Coulomb potentials
• Relating pseudospin and spin symmetries through chiral transformation with tensor interaction
• Novel quasi-exactly solvable models with anharmonic singular potentials