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International Journal of Modern Physics A

Noncommutative space effects on the Landau system for a neutral particle with induced electric dipole moment under a linear confining potential

Abdelali Saidi, Moulay Brahim Sedra

Published Jul 24, 2019• 8 citations
Publisher

Abstract

In this contribution, we study the effects of space noncommutativity on the Landau system for a neutral particle with induced electric dipole moment subject to a linear confining potential. We analytically solve the Schrödinger equation and obtain the complete set of energy levels and the corresponding radial wave functions for the system in terms of the noncommutativity parameter [Formula: see text].

DOI
10.1142/s0217751x1950115x

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In this contribution, we study the effects of space noncommutativity on the Landau system for a neutral particle with induced electric dipole moment subject to a linear confining potential. We analytically solve the Schrödinger equation and obtain the complete set of energy levels and the corresponding radial wave functions for the system in terms of the noncommutativity parameter [Formula: see text].
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.
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.
We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric qaudrupole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field, we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations both on a noncommutative space and a noncommutative phase space, we obtain quantum phases of the electric quadrupole moment, respectively. We demonstrate that these phases are geometric and dispersive.
In this work we investigate which radial field configuration yields bound states for neutral particles showing non-zero magnetic and electric dipole moments. The main result is that, in contrast with previous works, the Landau analog levels only exist if these radial magnetic and electric external fields are proportional to the third power of distance, not proportional to the distance. We derive the wave functions and the energy levels in the context of commutative and non-commutative quantum mechanics. We also show that, in the case of non-commutative phase space, these harmonic oscillator like spectrum do exist even if there is no external radial magnetic and electric fields. They are only consequence of the non-commutativity in the momenta.