From the generalized Morse potential to a unified treatment of the three-dimensional singular harmonic oscillator and singular Coulomb potentials

by Dr António Castro (Universidade Estadual Paulista)

Wednesday 19 Oct 2016, 14:00 → 15:00 Portugal

Sala de Conferências (Departamento de Física)

Bound-state solutions of the singular harmonic oscillator and singular Coulomb potentials in three dimensions are generated in a simple way from the solutions of the one-dimensional generalized Morse potential. The nonsingular harmonic oscillator and nonsingular Coulomb potentials with their additional accidental degeneracies are obtained as particular cases. Added bonuses from these mappings are the straightforward determination of the critical attractive singular potential, the proper boundary condition on the radial eigenfunction at the origin and the inexistence of bound states in a pure inversely quadratic potential.