On statistical mechanics in noncommutative spaces

We study the formulation of quantum statistical mechanics in noncommutative spaces. We construct microcanonical and canonical ensemble theory in noncommutative spaces. We consider for illustration some basic and important examples in the framework of noncommutative statistical mechanics : (i). An electron in a magnetic field. (ii). A free particle in a box. (iii). A linear harmonic oscillator.Comment: 9 pages, no figure

Scattering in Noncommutative Quantum Mechanics

We derive the correction due to noncommutativity of space on Born approximation, then the correction for the case of Yukawa potential is explicitly calculated. The correction depends on the angle of scattering. Using partial wave method it is shown that the conservation of the number of particles in elastic scattering is also valid in noncommutative spaces which means that the unitarity relation is held in noncommutative spaces. We also show that the noncommutativity of space has no effect on the optical theorem. Finally we study Gaussian function potential in noncommutative spaces which generates delta function potential as $\theta \to 0$.Comment: 7 Pages, no figure, accepted for publication in Modern Physics Letters

Hyperfine splitting in noncommutative spaces

We study the hyperfine splitting in the framework of the noncommutative quantum mechanics (NCQM) developed in the literature. The results show deviations from the usual quantum mechanics. We show that the energy difference between two excited F = I + 1/2 and the ground F = I - 1/2 states in a noncommutative space (NCS) is bigger than the one in the commutative case, so the radiation wavelength in NCSs must be shorter than the radiation wavelength in commutative spaces. We also find an upper bound for the noncommutativity parameter.Comment: No figure