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Journal of Mathematical Physics

Some aspects of the interaction of a magnetic quadrupole moment with an electric field in a rotating frame

I. C. Fonseca, K. Bakke

Published Oct 1, 2017• 16 citations
Publisher

Abstract

From the interaction between the magnetic quadrupole moment of a neutral particle (atom or molecule) with a radial electric field, a uniform effective magnetic field perpendicular to the plane of motion of the neutral particle appears. In addition, it is considered that the presence of a scalar potential is proportional to the radial distance and noninertial effects that stem from a rotating reference frame. Then, analytical solutions to the Schrödinger equation are obtained, where it is shown that the Landau-type levels are modified, and the allowed values of the cyclotron frequency are determined by the angular velocity of the rotating frame, the parameter associated with the scalar potential proportional to the radial distance and the quantum numbers of the system.

DOI
10.1063/1.5001564

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From the interaction between the magnetic quadrupole moment of a neutral particle (atom or molecule) with a radial electric field, a uniform effective magnetic field perpendicular to the plane of motion of the neutral particle appears. In addition, it is considered that the presence of a scalar potential is proportional to the radial distance and noninertial effects that stem from a rotating reference frame. Then, analytical solutions to the Schrödinger equation are obtained, where it is shown that the Landau-type levels are modified, and the allowed values of the cyclotron frequency are determined by the angular velocity of the rotating frame, the parameter associated with the scalar potential proportional to the radial distance and the quantum numbers of the system.
Quantum effects on a neutral particle (atom or molecule) with an induced electric dipole moment are investigated when it is subject to the Kratzer potential and a scalar potential proportional to the radial distance. In addition, this neutral is placed in a region with electric and magnetic fields. This system is analysed in both non-rotating and rotating reference frames. Then, it is shown that bound state solutions to the Schrödinger equation can be achieved and, in the search for polynomial solutions to the radial wave function, a restriction on the values of the cyclotron frequency is analysed in both reference frames.
The behaviour of a neutral particle (atom, molecule) with an induced electric dipole moment in a region with a uniform effective magnetic field under the influence of the Kratzer potential (Kratzer 1920 Z. Phys. 3 , 289–307. ( doi:10.1007/BF01327754 )), and rotating effects is analysed. It is shown that the degeneracy of the Landau-type levels is broken and the angular frequency of the system acquires a new contribution that stems from the rotation effects. Moreover, in the search for bound state solutions, it is shown that the possible values of this angular frequency of the system are determined by the quantum numbers associated with the radial modes and the angular momentum, the angular velocity of the rotating frame and by the parameters associated with the Kratzer potential.
We analyze the interaction of the magnetic quadrupole moment of a neutral particle with magnetic and electric fields around a cylindrical cavity in a rotating reference frame. In contrast to the energy levels yielded by a Coulomb-type potential that stems from the interaction of the magnetic quadrupole moment with a nonuniform magnetic field, we show that the effects of rotation break the degeneracy of the energy levels. Moreover, we show that the effects of rotation can gives rise to an Aharonov-Bohm-type effect. Further, we discuss the appearance of persistent currents and the revival time.
We study the appearance of an Aharonov–Bohm-type effect around a cylindrical cavity in a magnetic quadrupole moment system in a rotating reference frame. The analogue of the Aharonov–Bohm-type effect of bound states arises from the interaction of the magnetic quadrupole moment of a neutral particle with an induced electric field when the neutral particle is subject to an attractive inverse-square-type potential, which in turn stems from the interaction of the magnetic quadrupole moment of a neutral particle with a magnetic field. We also discuss how the effects of rotation modify the degeneracy of the energy levels in contrast to the case of absence of rotation. Besides this, we calculate the revival time and the persistent currents.
The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is that it gives rise to an analogue of a spinless particle subject to the doubly anharmonic oscillator. Then, it is shown that analytical solutions to the Schrödinger equation can be obtained. Another point raised is that the quantum effects on the induced electric dipole moment can be observed if the uniform magnetic field possesses a discrete set of values.