Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

2015 ◽  
Vol 362 ◽  
pp. 83-117 ◽  
Author(s):  
V.G. Ibarra-Sierra ◽  
J.C. Sandoval-Santana ◽  
J.L. Cardoso ◽  
A. Kunold
Keyword(s):  
Charged Particle ◽  
Harmonic Oscillator ◽  
Electromagnetic Fields ◽  
Algebraic Approach ◽  
Time Dependent

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.

On the Quantization Problem of a Driven Harmonic Oscillator with Time Dependent Mass and Frequency

2003 ◽  
Vol 17 (18) ◽  
pp. 983-990 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Present Solution ◽  
Quadratic Hamiltonian ◽  
Dependent Mass ◽  
Quantization Problem

The quantization of a driven harmonic oscillator with time dependent mass and frequency (DHTDMF) is considered. We observe that the driven term has no influence on the quantization of the oscillator. It is found that the DHTDMF corresponds the general quadratic Hamiltonian. The present solution is critically compared with existing solutions of DHTDMF.

scholarly journals Time-dependent propagator for an-harmonic oscillator with quartic term in potential

2021 ◽  
Vol 62 (2) ◽  
pp. 023501
Author(s):  
J. Boháčik ◽  
P. Prešnajder ◽  
P. Augustín
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Quartic Term
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