Motion of Charged Particle in Electric and Magnetic Fields in 3D Noncommutative Spaces and Related Problems

Abstract

In three-dimensional noncommutative phase space, the energy spectrum and wave functions for the motion of a charged particle in a magnetic field are derived. Due to the momentum-momentum noncommutativity, the particle feels an effective magnetic field in a new direction. When an external electric field perpendicular to this effective magnetic field is applied, the Hall conductivity can be calculated. To get the Hall conductivity, one should define the electric currents from the probability currents in quantum mechanics rather than extending the classical electric currents to quantum mechanics directly. When the electric field is not perpendicular to the effective magnetic field, it is difficult to define the Hall conductivity.

Entropy and Information of a harmonic oscillator in a time-varying electric field in 2D and 3D noncommutative spaces

“…Investigations of the quantum motion of harmonic oscillators in the presence of magnetic and electric fields in noncommutative backgrounds have also been reported [11][12][13][14][15][16][17]. In Ref.…”