PDM-charged particles in PD-magnetic plus Aharonov–Bohm flux fields: Unconfined “almost-quasi-free” and confined in a Yukawa plus Kratzer exact solvability

Abstract

Using azimuthally symmetrized cylindrical coordinates, we consider some positiondependent mass (PDM) charged particles moving in position-dependent (PD) magnetic and Aharonov-Bohm flux fields. We focus our attention on PDM-charged particles with m ( − → r ) = g (ρ) = η f (ρ) exp (−δρ) (i.e., the PDM is only radially dependent) moving in an inverse power-law-type radial PD-magnetic fieldsUnder such settings, we consider two almost-quasi-free PDM-charged particles (i.e., no interaction potential, V ( − → r ) = 0) endowed with g (ρ) = η/ρ and g (ρ) = η/ρ 2 . Both yield exactly solvable Schrödinger equations of Coulombic nature but with different spectroscopic structures. Moreover, we consider a Yukawa-type PDM-charged particle with g (ρ) = η exp (−δρ) /ρ moving not only in the vicinity of the PD-magnetic and Aharonov-Bohm flux fields but also in the vicinity of a Yukawa plus a Kratzer type potential force field V (ρ) = −V• exp (−δρ) /ρ−V 1 /ρ+V 2 /ρ 2 . For this particular case, we use the Nikiforov-Uvarov (NU) method to come out with exact analytical eigenvalues and eigenfunctions. Which, in turn, recover those of the almost-quasi-free PDM-charged particle with g (ρ) = η/ρ for V• = V 1 = V 2 = 0 = δ.

PDM Klein-Gordon oscillators in cosmic string spacetime in magnetic and Aharonov-Bohm flux fields within the Kaluza-Klein theory

“…where a uniform magnetic field is manifested in the z-direction through B = ∇ × A = (κ −1 B • /α) ẑ, and the Aharonov-Bohm flux field Φ is indulged in the second term of A ϕ [6,12,60,61]. Here, we have used A = A 1 + A 2 so that…”

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.…”

Isochronous $n$-dimensional nonlinear PDM-oscillators: linearizability, invariance and exact solvability

“…Which is, in fact, a very interesting equation for both physics and mathematics [1][2][3][4][5][6][7][8][9][10][11]. The linearizability and isochronicity of which have invited a vast number of interesting research studies in many fields (c.f., e.g., [35][36][37][38][39][40][41][42][43][44][45]). Tiwari et al [2] and Lakshmanan and Chandrasekar [3], for example, have used Lie point symmetries and asserted that in the case of eight parameter symmetry group, the one-dimensional quadratic Liénard type equation ( 3) is linearizable and isochronic.…”