scholarly journals SCATTERING IN NONCOMMUTATIVE QUANTUM MECHANICS

2005 ◽  
Vol 20 (13) ◽  
pp. 1013-1020 ◽  
Author(s):  
S. A. ALAVI
Keyword(s):  
Yukawa Potential ◽  
Gaussian Function ◽  
Delta Function ◽  
Optical Theorem ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Spaces ◽  
Partial Wave Method ◽  
Noncommutative Quantum ◽  
Function Potential ◽  
Number Of Particles

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 θ → 0.

scholarly journals From Feynman proof of Maxwell equations to noncommutative quantum mechanics

2007 ◽  
Vol 70 ◽  
pp. 012004 ◽  
Author(s):  
A Bérard ◽  
H Mohrbach ◽  
J Lages ◽  
P Gosselin ◽  
Y Grandati ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Maxwell Equations ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Quantum

scholarly journals Non-Hermitian noncommutative quantum mechanics

2019 ◽  
Vol 134 (7) ◽  
Author(s):  
J. F. G. dos Santos ◽  
F. S. Luiz ◽  
O. S. Duarte ◽  
M. H. Y. Moussa
Keyword(s):  
Quantum Mechanics ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Quantum

scholarly journals FERMIONIC DUAL OF ONE-DIMENSIONAL BOSONIC PARTICLES WITH DERIVATIVE DELTA FUNCTION POTENTIAL

2010 ◽  
Vol 25 (09) ◽  
pp. 715-725
Author(s):  
B. BASU-MALLICK ◽  
TANAYA BHATTACHARYYA
Keyword(s):  
Center Of Mass ◽  
Delta Function ◽  
Bose Gas ◽  
Duality Relation ◽  
Coupling Constant ◽  
Range Interaction ◽  
Fermionic System ◽  
One Dimensional ◽  
Zero Range ◽  
Function Potential

We investigate the boson–fermion duality relation for the case of quantum integrable derivative δ-function Bose gas. In particular, we find a dual fermionic system with nonvanishing zero-range interaction for the simplest case of two bosonic particles with derivative δ-function interaction. The coupling constant of this dual fermionic system becomes inversely proportional to the product of the coupling constant of its bosonic counterpart and the center-of-mass momentum of the corresponding eigenfunction.

scholarly journals A Noncommutative Model of Cosmology with Two Metrics

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 435
Author(s):  
Horacio Falomir ◽  
Jorge Gamboa ◽  
Fernando Mendez
Keyword(s):  
Quantum Mechanics ◽  
Dark Energy ◽  
Equation Of State ◽  
Point Of View ◽  
Classical Analog ◽  
Noncommutative Quantum Mechanics ◽  
Friedmann Robertson Walker ◽  
Noncommutative Quantum

We propose a bicosmology model which reduces to the classical analog of noncommutative quantum mechanics. From this point of view, one of the sources in the so modified Friedmann-Robertson- Walker equations is a kind of dark energy governed by a Chapligyn-like equation of state. The parameters of noncommutativity θ and B are interpreted in terms of the Planck area and a magnetic-like field, which presumably acts as a seed for magnetogenesis.

INVARIANT EIGEN-OPERATOR METHOD OF DERIVING ENERGY-LEVEL GAP FOR NONCOMMUTATIVE QUANTUM MECHANICS

2005 ◽  
Vol 20 (09) ◽  
pp. 691-698 ◽  
Author(s):  
SI-CONG JING ◽  
HONG-YI FAN
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Operator Method ◽  
Simple Algebra ◽  
New Method ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Quantum

We propose a new method to derive energy-level gap for Hamiltonians in the context of noncommutative quantum mechanics (NCQM). This method relies on finding invariant eigen-operators whose commutators with Hamiltonian are still the operators themselves but with some eigenvalue-like coefficients, which correspond to the energy-level gaps of the systems. Based on this method, only after some simple algebra, we derive the energy-level gaps for several important systems in NCQM, and most of these results have not been reported in literature so far.

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