Scalar–vector–pseudoscalar Cornell potential for a spin-1/21/2 particle under spin and pseudospin symmetries: 1+11+1 dimensions

• We investigate the Dirac equation with the scalar–vector–pseudoscalar Cornell potential.
• The solutions are discussed in view of spin and pseudospin symmetry limits.
• The energy levels and the wave function are presented in Heun biconfluent equations.

The Cornell potential consists of Coulomb and linear potentials, i.e. −a/x+bx−a/x+bx, that has received a great deal of attention in particle and nuclear physics. In this paper, we present exact solutions of the Dirac equation with the mixed scalar–vector–pseudoscalar Cornell potential under spin and pseudospin symmetry limits. The corresponding eigenfunctions are given in the form of the biconfluent Heun polynomials.