Bound states of the Dirac equation with non-central scalar and vector potentials: a modified double ring-shaped generalized Cornell potential

In this paper, the bound state solutions and their corresponding relativistic energy eigenvalues of the Dirac equation are calculated with non-central scalar and vector potentials, a modified double ring-shaped generalized Cornell potential, in the framework of quasi-exactly solvable problems. In the case of spin symmetry, the Dirac equation is transformed into a Schrodinger-like equation. Using the separation of variables, we compute the angular parts of the solutions, of the corresponding Schrodinger-like equation, via the functional Bethe ansatz, and the radial part is determined by solving the biconfluent Heun differential equation.

Automated summary

This paper calculates the bound state solutions and energy eigenvalues of the Dirac equation with non-central scalar and vector potentials using a modified double ring-shaped generalized Cornell potential in the framework of quasi-exactly solvable problems. When spin symmetry is present, the Dirac equation is transformed into a Schrodinger-like equation, with the angular parts of the solutions computed using functional Bethe ansatz and the radial part determined by solving the biconfluent Heun differential equation.