scholarly journals Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation

2015 ◽  
Vol 24 (11) ◽  
pp. 1550087 ◽  
Author(s):  
B. J. Falaye ◽  
Shi-Hai Dong ◽  
K. J. Oyewumi ◽  
K. F. Ilaiwi ◽  
S. M. Ikhdair
Keyword(s):  
Energy Spectrum ◽  
Harmonic Oscillator ◽  
Commutation Relation ◽  
Uncertainty Relation ◽  
Minimal Length ◽  
Harmonic Oscillators ◽  
Relativistic Energy ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Modified Dirac Equation

We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation [Formula: see text]. In the nonrelativistic (NR) limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the [Formula: see text] algebra is satisfied by the operators [Formula: see text] and [Formula: see text].

scholarly journals The Minimal Length and the Shannon Entropic Uncertainty Relation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Pouria Pedram
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Commutation Relation ◽  
Deformation Parameter ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Adjoint Representation ◽  
Minimal Length ◽  
Entropic Uncertainty Relation ◽  
Ordinary Quantum

In the framework of the generalized uncertainty principle, the position and momentum operators obey the modified commutation relationX,P=iħ1+βP2, whereβis the deformation parameter. Since the validity of the uncertainty relation for the Shannon entropies proposed by Beckner, Bialynicki-Birula, and Mycielski (BBM) depends on both the algebra and the used representation, we show that using the formally self-adjoint representation, that is,X=xandP=tan⁡βp/β, where[x,p]=iħ, the BBM inequality is still valid in the formSx+Sp≥1+ln⁡πas well as in ordinary quantum mechanics. We explicitly indicate this result for the harmonic oscillator in the presence of the minimal length.

scholarly journals Stability analysis of an ensemble of simple harmonic oscillators

2021 ◽  
pp. 2150034
Author(s):  
R. K. Thakur ◽  
B. N. Tiwari ◽  
R. Nigam ◽  
Y. Xu ◽  
P. K. Thiruvikraman
Keyword(s):  
Partition Function ◽  
Harmonic Oscillator ◽  
Geometric Phase ◽  
Hessian Matrix ◽  
Harmonic Oscillators ◽  
Real Numbers ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
The Stability ◽  
Embedding Function

In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to variations of the parameters, viz. the mass, temperature and the frequency of oscillators. Here, we introduce the Hessian matrix of the partition function as the model embedding function from the space of parameters to the set of real numbers. In this framework, we classify the regions in the parameter space of the harmonic oscillator fluctuations where they yield a stable statistical configuration. The mechanism of stability follows from the notion of the fluctuation theory. In Secs. ?? and ??, we provide the nature of local and global correlations and stability regions where the system yields a stable or unstable statistical basis, or it undergoes into geometric phase transitions. Finally, in Sec. ??, the comparison of results is provided with reference to other existing research.

scholarly journals Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation

2015 ◽  
Vol 30 (35) ◽  
pp. 1550206 ◽  
Author(s):  
Zachary Lewis ◽  
Ahmed Roman ◽  
Tatsu Takeuchi
Keyword(s):  
Harmonic Oscillator ◽  
Commutation Relation ◽  
Classical Limit ◽  
Uncertainty Relation ◽  
Minimal Length ◽  
Positive Energy ◽  
Positive Mass ◽  
Negative Mass ◽  
Energy Eigenstates ◽  
Theory Comparison

We calculate the uncertainties in the position and momentum of a particle in the 1D potential [Formula: see text], [Formula: see text], when the position and momentum operators obey the deformed commutation relation [Formula: see text], [Formula: see text]. As in the harmonic oscillator case, which was investigated in a previous publication, the Hamiltonian [Formula: see text] admits discrete positive energy eigenstates for both positive and negative mass. The uncertainties for the positive mass states behave as [Formula: see text] as in the [Formula: see text] limit. For the negative mass states, however, in contrast to the harmonic oscillator case where we had [Formula: see text], both [Formula: see text] and [Formula: see text] diverge. We argue that the existence of the negative mass states and the divergence of their uncertainties can be understood by taking the classical limit of the theory. Comparison of our results is made with previous work by Benczik.

scholarly journals Exact Solutions of the Mass-Dependent Klein-Gordon Equation with the Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Bahar ◽  
F. Yasuk
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Oscillator Potential ◽  
Ansatz Method ◽  
Harmonic Oscillator Potential ◽  
Klein Gordon ◽  
Dependent Mass ◽  
Mass Dependent ◽  
Klein Gordon Equation

Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

GROUND STATE OF N HARMONICALLY BOUND ANYONS IN A MAGNETIC FIELD

1992 ◽  
Vol 07 (38) ◽  
pp. 3593-3600
Author(s):  
R. CHITRA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Harmonic Oscillator ◽  
Ground State ◽  
Harmonic Frequency ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Thomas Fermi ◽  
Large N ◽  
The Magnetic Field

The properties of the ground state of N anyons in an external magnetic field and a harmonic oscillator potential are computed in the large-N limit using the Thomas-Fermi approximation. The number of level crossings in the ground state as a function of the harmonic frequency, the strength and the direction of the magnetic field and N are also studied.

scholarly journals NEW FEATURES IN SUPERSYMMETRY BREAKDOWN IN QUANTUM MECHANICS

1996 ◽  
Vol 11 (19) ◽  
pp. 1563-1567 ◽  
Author(s):  
BORIS F. SAMSONOV
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Mechanical Model ◽  
State Energy ◽  
Vacuum State ◽  
Quantum Mechanical ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Quantum Mechanical Model ◽  
Higher Derivative

The supersymmetric quantum mechanical model based on higher-derivative supercharge operators possessing unbroken supersymmetry and discrete energies below the vacuum state energy is described. As an example harmonic oscillator potential is considered.

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