Approximate Solutions to the Klein-Fock-Gordon Equation for the Sum of Coulomb and Ring-Shaped-Like Potentials

Abstract EN

We consider the quantum mechanical problem of the motion of a spinless charged relativistic particle with mass M, described by the Klein-Fock-Gordon equation with equal scalar Sr→ and vector Vr→ Coulomb plus ring-shaped potentials.

It is shown that the system under consideration has both a discrete at EMc2 energy spectra.

We find the analytical expressions for the corresponding complete wave functions.

A dynamical symmetry group SU1,1 for the radial wave equation of motion is constructed.

The algebra of generators of this group makes it possible to find energy spectra in a purely algebraic way.

It is also shown that relativistic expressions for wave functions, energy spectra, and group generators in the limit c⟶∞ go over into the corresponding expressions for the nonrelativistic problem.