Study of Certain Atomic Systems in the Context of Generalized Quantum Mechanics

Abstract

In this thesis, we conducted an analytical study at the atomic scale of two-dimensional relativistic deformed bosonic and fermionic oscillator equations for charged particles subject to the effect of a uniform magnetic field. In the first stage, we consider the presence of a minimal uncertainty in momentum caused by the anti-deSitter space model and we use the Nikiforov Uvarov method (NU) to solve the system. The exact energy eigenvalues and the corresponding wave functions are obtained using Jacobi polynomials, and we find that the deformed spectrum remains discrete even for large values of the principal quantum number. In addition, after evaluating the thermal properties, we find that they have been affected by the deformation of the space at high-temperature regime. In the second stage, we solve the same equations in the non-commutative space using a direct method to obtain the energy spectrums and the wave functions, we detect that the study has similar behaviors to the Landau problem in commutative space. Then, the outcomes of the thermal properties show that the systems have been influenced by the NC space. At the last stage, we generalize both deformations in the relativistic equations, and we solve the systems using the NU method hence we obtained the exact energy spectrums and the wave functions by applying the Jacobi polynomials; in the end, we examine the thermal properties which have been influenced by the two deformations.