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

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 effects of dislocation as well PDM settings on energy levels some PDM-quantum mechanical systems. In so doing, use a power-law type positive-valued dimensionless scalar multiplier f(r)=\lambda r^{\sigma }$$ (which manifestly introduces metaphoric notion PDM-Schödinger particles). Next, subject such to magnetic Aharonov–Bohm flux fields. exact or conditionally eigenvalues eigenfunctions for $$V(r)=0$$ $$V(r) =a+b\,r+c\,r^{2}$$ .