Position-dependent mass Schrödinger particles in space-like screw dislocation: associated degeneracies and magnetic and Aharonov–Bohm flux fields effects

Abstract

We consider non-relativistic position-dependent mass (PDM) Schödinger particles moving in an elastic medium with space-like screw dislocation. Within the cylindrical coordinates $$\left( r,\phi ,z\right) $$ , we study and report the effects of screw dislocation as well as PDM settings on the energy levels of some PDM-quantum mechanical systems. In so doing, we use a power-law type positive-valued dimensionless scalar multiplier $$ f(r)=\lambda r^{\sigma }$$ (which manifestly introduces the metaphoric notion of PDM-Schödinger particles). Next, we subject such PDM particles to magnetic and Aharonov–Bohm flux fields. We report exact or conditionally exact eigenvalues and eigenfunctions for $$V(r)=0$$ and $$V(r) =a+b\,r+c\,r^{2}$$ .