Quantum Effects on an Atom with a Magnetic Quadrupole Moment in a Region with a Time-Dependent Magnetic Field

Abstract

The quantum description of an atom with a magnetic quadrupole moment in the presence of a time-dependent magnetic field is analysed. It is shown that the time-dependent magnetic field induces an electric field that interacts with the magnetic quadrupole moment of the atom and gives rise to a Landau-type quantization. It is also shown that a time-independent Schrödinger equation can be obtained, i.e., without existing the interaction between the magnetic quadrupole moment of the atom and the time-dependent magnetic field, therefore, the Schrödinger equation can be solved exactly. It is also analysed this system subject to scalar potentials.

Confluent hypergeometric expansions of the confluent Heun function governed by two-term recurrence relations

“…Resolving the recurrence (10), the coefficients of expansion ( 2) are explicitly written in terms of the gamma functions as ( 0 1 c  )…”

“…Currently, the Heun equations are encountered in so many branches of classical and nonclassical physics ranging from non-Newtonian liquid mechanics, rheology, surface physics, polymer physics, atomic and nuclear physics to general gravity, astronomy and cosmology, e.g., the dislocation theory and mass-step problem in quantum mechanics, time-dependent few-state models in quantum optics, quantum two-center problem in molecular physics, surface polaritons, lattice systems in statistical mechanics, theory of black holes, etc., that it is difficult to give a classification of all relevant problems (see, e.g., [5][6][7][8][9][10][11][12][13][14][15][16][17]).…”

Expansions of the Solutions of the General Heun Equation Governed by Two-Term Recurrence Relations for Coefficients

“…The general Heun equation [1][2][3], which is the most general second-order linear ordinary differential equation having four regular singular points, is currently widely encountered in physics and mathematics research (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein). However, this equation is much less studied than its immediate predecessor, the Gauss hypergeometric equation, which is the most general equation having three regular singular points.…”

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

“…For example, the Aharonov-Bohm effect [1][2][3][4] for a charged particle, the scalar Aharonov-Bohm and He-Mckellar-Willens effects [5][6][7][8][9][10][11], for bound states [12], and Landau quantization [13][14][15][16] for an electric dipole moment of a neutral particle. Furthermore, recent studies have investigated the interaction between the quadrupole moments of neutral particle and external fields in several quantum systems such as geometric quantum phases [17], noncommutative quantum mechanics [19], nuclear structure [20,21], atomic systems [22][23][24][25][26][27], molecular systems [28][29][30], and Landau quantization [18,[31][32][33].…”