A generalized Coulomb problem for a spin-1/2 fermion

by Vitor Bentes Mendrot (Faculdade de Engenharia de Guaratinguetá, Departamento de Física, UNESP)

Wednesday 11 Mar 2026, 14:00 → 15:00 Portugal

Sala de Conferências (Departamento de Física FCTUC)

We study the Dirac equation in 3+1-dimensions with a general combination of scalar, vector and tensor interactions with unrestricted strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the tensor coupling a constant term is also included, since this gives rise to an effective Coulomb potential which is necessary for the creation of bound states in a pure tensor coupling configuration. The exact bound-state solutions for this generalized Coulomb problem are computed by exploiting some freedom in the choice of coefficients for the Ansätze of the radial functions, which leads to wave functions in terms of generalized Laguerre polynomials. From the quantization condition, the exact energy spectrum is also determined and its dependence on the parameters of the potentials is discussed. We show that similar features of the equations for the problem in the plane and the spherically symmetric problem allows a simple and direct mapping between them, thus we also provide the solution to the spherical Coulomb problem.