Position-dependent mass charged particles in magnetic and Aharonov–Bohm flux fields: separability, exact and conditionally exact solvability

Exact solution of the semiconfined harmonic oscillator model with a position-dependent effective mass in an external homogeneous field

“…Here again one needs to mention that different versions of nonrelativistic kinetic energy operators (3) exist for the case of effective mass changing with position. There are Gora-Williams, Zhu-Kroemer, von Roos kinetic energy operators [26][27][28] as well as kinetic energy operators based on the contact point transformation method [29][30][31][32] and non-Hermitian PT symmetric kinetic energy operators [33][34][35][36][37][38].…”

“…Our main goal was to show that the semiconfined quantum harmonic oscillator with position-dependent effective mass is exactly solvable even if it is under an external homogeneous field. We achieved this goal by obtaining analytical expressions of the energy spectrum (31) and normalized wavefunctions (32). In the following section, we are going to discuss some important properties of this model.…”

Landau quantization for an electric quadrupole moment of position-dependent mass quantum particles interacting with electromagnetic fields

“…We may now discuss the separability of the PDM Schrödinger equation (14) in the cylindrical coordinates (ρ, φ, z) and under azimuthal symmetrization. By assuming that the field configurations and that the PDM functions are only radially dependent [54,55,[59][60][61] (i,e., m ( − → r ) = M (ρ, φ, z) = g (ρ) ), the wavefunction can be written as…”

“…Not only because of its ordering ambiguity associated with the non-unique representation of the kinetic energy operator, but also because of its feasible applicability in many fields of physics. Recent studies on such PDM charged particles in constant magnetic fields [56][57][58][59][60], and position-dependent magnetic fields [61] are carried out (using different interaction potentials). To the best of our knowledge, however, no studies have ever been considered to discuss the quantum mechanical effects on PDM neutral particles possessing an electric quadrupole moment.…”

“…In so doing, we use the very recent result suggested by [58,59] for the PDM-minimal-coupling and the PDM-momentum operator. Furthermore, we discuss the possibility of achieving the Landau quantization for such a system, and the separability of the problem in the cylindrical coordinates (ρ, φ, z), under azimuthal symmetrization, by considering that the field configurations and the PDM settings are purely radial dependent as in [54,55,[59][60][61]. In section III, we discuss a Landau levels analog for an electric quadrupole moment interacting with an external magnetic field in the absence of electric field.…”