An alternative formulation of Hall effect and quantum phases in noncommutative space

Abstract

A recent method of constructing quantum mechanics in noncommutative coordinates, alternative to implying noncommutativity by means of star product is discussed. Within this approach we study Hall effect as well as quantum phases in noncommutative coordinates. The θ-deformed phases which we obtain are velocity independent.

Equivalence of curvature and noncommutativity in a physical space: Harmonic oscillator on sphere

“…Noncommutative quantum mechanics very soon earned its spot in different fields of physics because of the significant results which it can predict, from condensed matter topics such quantum Hall effect, [5][6][7] Aharonov-Bohm 8 and Aharonov-Casher effect 9 to recent developed concepts in quantum optics such as entanglement 10 and decoherence. 11 One of the best model which can demonstrate the physical results in an appropriate way is the harmonic oscillator.…”

Solutions of Klein-Gordon equation for the modified central complex potential in the symmetries of noncommutative quantum mechanics

“…In this paper, motivated bymany various recent studies for example the nonrenormalizable of the electroweak interaction,quantum gravity, string theory, the noncommutative relativistic quantum mechanics has attracted much attentionto physical researchers [15][16][17][18][19][20][21] .…”