A bound quantum particle in a Riemann–Cartan space with topological defects and planar potential

Starting from a continuum theory of defects, that is the analogous to three-dimensional Einstein–Cartan–Sciama–Kibble gravity, we consider a charged particle with spin 12 propagating in a uniform magnetic field coincident with a wedge dispiration of finite extent. We assume the particle is bound in the vicinity of the dispiration by long range attractive (harmonic) and short range (inverse square) repulsive potentials. Moreover, we consider the effects of spin-torsion and spin-magnetic field interactions. Exact expressions for the energy eigenfunctions and eigenvalues are determined. The limit, in which the defect region becomes singular, is considered and comparison with the electromagnetic Aharonov–Bohm effect is made.