scholarly journals Quantum particle motion on the surface of a helicoid in the presence of an harmonic oscillator

Physics Open ◽  
2020 ◽  
Vol 5 ◽  
pp. 100045
Author(s):  
Marcos C.R. Ribeiro ◽  
Márcio M. Cunha ◽  
Cleverson Filgueiras ◽  
Edilberto O. Silva
Keyword(s):  
Harmonic Oscillator ◽  
Particle Motion ◽  
Quantum Particle

scholarly journals Quantum particle motion in absorbing harmonic trap

2015 ◽  
Vol 90 (4) ◽  
pp. 441-446 ◽  
Author(s):  
B. G. Márkus ◽  
F. Márkus
Keyword(s):  
Particle Motion ◽  
Quantum Particle ◽  
Harmonic Trap

Factorization in the quantum mechanics with the generalized uncertainty principle

2015 ◽  
Vol 30 (23) ◽  
pp. 1550117 ◽  
Author(s):  
Won Sang Chung
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Perturbation Method ◽  
Commutation Relation ◽  
Uncertainty Principle ◽  
Quantum Particle ◽  
Generalized Uncertainty Principle ◽  
Factorization Method ◽  
Momentum Operator ◽  
Energy Eigenvalues

In this paper, we discuss the quantum mechanics with the generalized uncertainty principle (GUP) where the commutation relation is given by [Formula: see text]. For this algebra, we obtain the eigenfunction of the momentum operator. We also study the GUP corrected quantum particle in a box. Finally, we apply the factorization method to the harmonic oscillator in the presence of a minimal observable length and obtain the energy eigenvalues by applying the perturbation method.

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

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