Quasi-exact solvability of Dirac equation with Lorentz scalar potential. (English) Zbl 1097.81027

Summary: We consider exact/quasi-exact solvability of Dirac equation with a Lorentz scalar potential based on factorizability of the equation. Exactly solvable and sl(2)-based quasi-exactly solvable potentials are discussed separately in Cartesian coordinates for a pure Lorentz potential depending only on one spatial dimension, and in spherical coordinates in the presence of a Dirac monopole.


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81U15 Exactly and quasi-solvable systems arising in quantum theory


Dirac monopole
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