The quantum and Klein-Gordon oscillators in a non-commutative complex space and the thermodynamic functions

Abstract

In this work we study the quantum and Klein-Gordon oscillators in non-commutative complex space. We show that the quantum oscillator in non-commutative complex space obeys an equation similar to the equation of motion of an electron with spin in a commutative space in an external uniform magnetic field. Therefore the wave function $\psi (z,\bar{z})$ takes values in $C^4$, spin up, spin down, particle, antiparticle, a result which is obtained by the Dirac theory. We derive the thermodynamic functions associated to the partition function. We show that the non-commutativity affects energy at the high temperature limit. The Klein Gordon oscillator in non-commutative complex space also has a similar equation of motion to that a fermions with spin 1/2 in a commutative space in a constant magnetic field. The energy levels could be obtained by exact solution.

11 pages, no figures. International Journal of Theoretical Physics (2014)

References in corpus (3)

• A Gravity Theory on Noncommutative Spaces
• Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
• Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space

Cited by in corpus (2)

• Negative heat capacity for a Klein-Gordon oscillator in non-commutative complex phase space
• Entropy and Information of a harmonic oscillator in a time-varying electric field in 2D and 3D noncommutative spaces