Schrödinger oscillators in a deformed point-like global monopole spacetime and a Wu-Yang magnetic monopole: position-dependent mass correspondence and isospectrality

Abstract

We show that a specific transformation/deformation in a point-like global monopole (PGM) spacetime background would yield an effective position-dependent mass (PDM) Schrödinger equation (i.e., a von Roos PDM Schrödinger equation). We discuss PDM Schrödinger oscillators in a PGM spacetime in the presence of a Wu-Yang magnetic monopole. Within our transformed/deformed global monopole spacetime, we show that all PDM Schrödinger oscillators admit isospectrality and invariance with the constant mass Schrödinger oscillators in the regular global monopole spacetime in the presence of a Wu-Yang magnetic monopole. The exclusive dependence of the thermodynamical partition function on the energy eigenvalues manifestly suggests that the Schrödinger oscillators and the PDM Schrödinger oscillators share the same thermodynamical properties as mandated by their isospectrality. Moreover, we discuss the hard-wall effect on the energy levels of the PDM Schrödinger oscillators in a PGM spacetime without and with a Wu-Yang magnetic monopole. Drastic energy levels' shift-ups are observed as a consequence of such hard-wall effect.