scholarly journals An algebraic approach to a charged particle in a uniform magnetic field

2018 ◽  
Vol 64 (2) ◽  
pp. 127
Author(s):  
D. Ojeda-Guillén ◽  
M. Salazar-Ramírez ◽  
R.D. Mota ◽  
V.D. Granados
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Uniform Magnetic Field ◽  
Similarity Transformation ◽  
Algebraic Approach ◽  
Landau Gauge ◽  
Displacement Operator ◽  
Symmetric Gauge

We study the problem of a charged particle in a uniform magnetic field with two different gauges, known as Landau and symmetric gauges. By using a similarity transformation in terms of the displacement operator we show that, for the Landau gauge, the eigenfunctions for this problem are the harmonic oscillator number coherent states. In the symmetric gauge, we calculate the SU(1; 1) Perelomov number coherent states for this problem in cylindrical coordinates in a closed form. Finally, we show that these Perelomov number coherent states are related to the harmonic oscillator number coherent states by the contraction of the SU(1; 1) group to the Heisenberg-Weyl group.

scholarly journals Coherent State Quantization and Moment Problem

10.14311/1185 ◽  
2010 ◽  
Vol 50 (3) ◽  
Author(s):  
J. P. Gazeau ◽  
M. C. Baldiotti ◽  
D. M. Gitman
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Energy Spectrum ◽  
Phase Space ◽  
Coherent State ◽  
Moment Problem ◽  
Coherent States ◽  
Uniform Magnetic Field ◽  
Classical Motion ◽  
Negative Numbers

Berezin-Klauder-Toeplitz (“anti-Wick”) or “coherent state” quantization of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity provided by the standard (or gaussian) coherent states. The construction of these states and their attractive properties are essentially based on the energy spectrum of the harmonic oscillator, that is on natural numbers. We follow in this work the same path by considering sequences of non-negative numbers and their associated “non-linear” coherent states. We illustrate our approach with the 2-d motion of a charged particle in a uniform magnetic field. By solving the involved Stieltjes moment problem we construct a family of coherent states for this model. We then proceed with the corresponding coherent state quantization and we show that this procedure takes into account the circle topology of the classical motion.

ATOMIC COHERENT STATES AS THE EIGENSTATES OF A TWO-DIMENSIONAL ANISOTROPIC HARMONIC OSCILLATOR IN A UNIFORM MAGNETIC FIELD

2009 ◽  
Vol 24 (38) ◽  
pp. 3129-3136 ◽  
Author(s):  
XIANG-GUO MENG ◽  
JI-SUO WANG ◽  
HONG-YI FAN
Keyword(s):  
Magnetic Field ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Uniform Magnetic Field ◽  
Hermite Polynomial ◽  
Entangled State ◽  
Two Dimensional ◽  
Entangled State Representation ◽  
Single Variable ◽  
State Representation

In the newly constructed entangled state representation embodying quantum entanglement of Einstein, Podolsky and Rosen, the usual wave function of atomic coherent state ∣τ〉 = exp (μJ+-μ*J-)∣j, -j〉 turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j, where j is the spin value. We then prove that a two-dimensional time-independent anisotropic harmonic oscillator in a uniform magnetic field possesses energy eigenstates which can be classified as the states ∣τ〉 in terms of the spin values j.

Hydromagnetic effects on non-Newtonian Hiemenz flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Magnetic Field ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Uniform Magnetic Field ◽  
Magnetic Parameter ◽  
Similarity Transformation ◽  
The Self ◽  
Free Boundary Value Problem ◽  
Uniqueness Of The Solution ◽  
Self Similar

Abstract The stagnation point flow of a non-Newtonian Reiner–Rivlin fluid has been studied in the presence of a uniform magnetic field. The technique of similarity transformation has been used to obtain the self-similar ordinary differential equations. In this paper, an attempt has been made to prove the existence and uniqueness of the solution of the resulting free boundary value problem. Monotonic behavior of the solution is discussed. The numerical results, shown through a table and graphs, elucidate that the flow is significantly affected by the non-Newtonian cross-viscous parameter L and the magnetic parameter M.

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