Commutative vs. Noncommutative Space Statistical Properties of Two-Dimensional Harmonic Oscillator in Magnetic Field

Abstract

The Schrodinger equation and its solutions are still a challenging subject in physics. Just as many other areas of science, where we have to solve a differential equation to obtain the required information, we have to first solve the building block of nonrelativistic quantum mechanics. In doing so, we have to use numerical and analytical techniques depending on the structure of the equation. In particular, the analytical approaches are attractive as they provide a deeper and more touchable insight into the physics of the problem [1–6]. Cooper et al. reviewed the theoretical formulation of supersymmetry quantum mechanics and discussed its applications in dealing with both relativistic and nonrelativistic equations of quantum mechanics [7]. Ciftci et al. used the asymptotic iteration method for finding solutions of the Schrodinger equation [8]. Slater considered a simplification of the Hartree–Fock method to analyze the related problems [9]. Stevenson applied the optimized perturbation theory to the field [10]. Dong et al. proposed the quasi-exact solutions of the Schrodinger equation via the ansatz technique which is a quasi-exact approach [11]. Another frequently used tool is the Nikiforov–Uvarov (NU) technique which transforms classes of equations of mathematical physics into hypergeometric form. A reason of recent renewed interests in the wave equations of quantum mechanics is the implications of fundamental theories such as string theory. To be more precise, the noncommutative (NC) formulations of quantum mechanics and the proposition of the so-called minimal length, has motivated many recent studies on the quantum equations. The NC formulation, which is the focus of the present work, originates from fundamental theories