Dirac Equations with Confining Potentials

Abstract

This paper is devoted to a study of relativistic eigenstates of Dirac particles which are simultaneously bound by a static Coulomb potential and added linear confining potentials. It has recently been shown that, despite the addition of radially symmetric, linear confining potentials, some specific bound-state energies surprisingly retain their exact Dirac--Coulomb values (in the sense of an "exact symmetry"). This observation raises pertinent questions as to the generality of the cancellation mechanism. A Foldy-Wouthuysen transformation is used to find the relevant nonrelativistic physical degrees of freedom, which include additional spin-orbit couplings induced by the linear confining potentials. The matrix elements of the effective operators obtained from the scalar, and time-like confining potentials mutually cancel for specific ratios of the prefactors of the effective operators, which must be tailored to the cancellation mechanism. The result of the Foldy-Wouthuysen transformation is used to explicitly show that the cancellation is accidental and restricted (for a given Hamiltonian) to only one reference state, rather than traceable to a more general relationship among the obtained effective low-energy operators. Furthermore, we show that the cancellation mechanism does not affect anti-particle (negative-energy) states.

11 pages; RevTeX

Cited by in corpus (4)

• Aharonov-Bohm effect for bound states in relativistic scalar particle systems in a spacetime with a space-like dislocation
• On a relativistic scalar particle subject to a Coulomb-type potential given by Lorentz symmetry breaking effects
• The generalized Klein-Gordon oscillator with position-dependent mass in a particular Gödel-type space-time
• On the Majorana fermion subject to a linear confinement