On the spectra of noncommutative 2D harmonic oscillator

Rotational Symmetry and Gauge Invariant Degeneracies on 2D Noncommutative Plane

“…A close inspection reveals that the eigenvalues and eigenstates shown in (3.1) and (3.2) are quite familiar in some literature (e.g [9,23]) as it is actually the solution of the eigenvalue problem involving noncommutative planar isotropic harmonic oscillator if the coordinates transformation used is the generalized Bopp shift or Seiberg-Witten map. The energy eigenvalues of the system for the first few lower quantum number pairs are shown in Table 1.…”

“…(2.35) and L m l nr is the Laguerre polynomials [9,28]. Realize that there is a condition to be satisfied to the solution of the eigenvalue problem before it can really be applied to a physical system.…”

“…There are numerous works which tackle the issue of the one particle sector of noncommutative field theories i.e, noncommutative quantum mechanics (NCQM) in different settings. This includes harmonic oscillator [7,8,9], magnetic field [10,11,12,13,14], hydrogen atom [15], central potential [16,17], Landau problem [18], Klein-Gordon and Dirac oscillators [19,20,21], Aharonov-Casher effect [22] and the list goes on. One of the authors [23] studied a system of spinless electrons moving in a 2D noncommutative space in the presence of a perpendicular magnetic field and confining harmonic potential.…”

(2+1)-Dimensional Duffin-Kemmer-Petiau Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Noncommutative Space

“…The noncommutativity of space-time coordinates was first introduced by Snyder [29] aiming to improve the problem of infinite self-energy in quantum field theory, and the noncommutative geometry has been put forward because of the discovery in string theory and matrix model of M-theory [30]. Recently, various aspects of both NC classical [31] and quantum [32] mechanics have been extensively studied devoted to exploring the role of NC parameter in the physical observables [33][34][35][36][37][38][39][40]. Recently, the effect of the quantum gravity on the quantum mechanics by modifying the basic commutators among the canonical variables has been an attractive topic, therefore the combination of the minimal length uncertainty relation and the noncommutative space commutation relations is a colorful problem.…”

On the Thermodynamic Properties of the Spinless Duffin-Kemmer-Petiau Oscillator in Noncommutative Plane

“…Recently, various aspects of both NC classical [17] and quantum [18] mechanics have been investigated by large number of papers, devoted to exploring the role of NC parameter in the physical observables. For example, classical Newton mechanics in the noncommutative space was studied in [19,20], a particle confined by a quadratic potential in the generalized noncommutative plane was investigated from both the classical and the quantum aspects in [21], the noncommutative harmonic oscillators were discussed in detail in [22][23][24], and [25] studied the Aharonov-Bohm effect in a class of noncommutative theories.…”