On the quantum mechanical solutions with minimal length uncertainty

In this paper, we study two generalized uncertainty principles (GUPs) including [Formula: see text] and [Formula: see text] which imply minimal measurable lengths. Using two momentum representations, for the former GUP, we find eigenvalues and eigenfunctions of the free particle and the harmonic oscillator in terms of generalized trigonometric functions. Also, for the latter GUP, we obtain quantum mechanical solutions of a particle in a box and harmonic oscillator. Finally we investigate the statistical properties of the harmonic oscillator including partition function, internal energy, and heat capacity in the context of the first GUP.

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Some quantum mechanical solutions in nonrelativistic anti-Snyder framework

International Journal of Modern Physics A ◽

10.1142/s0217751x17501706 ◽

2017 ◽

Vol 32 (27) ◽

pp. 1750170 ◽

Cited By ~ 1

Author(s):

Homa Shababi ◽

Won Sang Chung

Keyword(s):

Neutron Star ◽

Harmonic Oscillator ◽

Free Particle ◽

Three Dimensions ◽

One Dimension ◽

Quantum Mechanical ◽

Momentum Representation ◽

Eigenvalues And Eigenfunctions

In this paper, we investigate nonrelativistic anti-Snyder model in momentum representation and obtain quantum mechanical eigenvalues and eigenfunctions. Using this framework, first, in one dimension, we study a particle in a box and the harmonic oscillator problems. Then, for more investigations, in three dimensions, the quantum mechanical eigenvalues and eigenfunctions of a free particle problem and the radius of the neutron star are obtained.

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The Damped Harmonic Oscillator at the Classical Limit of the Snyder-de Sitter Space

Journal of Mathematics Research ◽

10.5539/jmr.v13n2p1 ◽

2021 ◽

Vol 13 (2) ◽

pp. 1

Author(s):

Lat´evi M. Lawson ◽

Ibrahim Nonkan´e ◽

Komi Sodoga

Keyword(s):

Harmonic Oscillator ◽

Classical Limit ◽

Minimal Length ◽

Poisson Brackets ◽

Canonical Transformations ◽

Trigonometric Functions ◽

De Sitter ◽

One Dimensional ◽

Damped Harmonic Oscillator ◽

Math Phys

Valtancoli in his paper entitled (P. Valtancoli, Canonical transformations and minimal length, J. Math. Phys. 56, 122107 2015) has shown how the deformation of the canonical transformations can be made compatible with the deformed Poisson brackets. Based on this work and through an appropriate canonical transformation, we solve the problem of one dimensional (1D) damped harmonic oscillator at the classical limit of the Snyder-de Sitter (SdS) space. We show that the equations of the motion can be described by trigonometric functions with frequency and period depending on the deformed and the damped parameters. We eventually discuss the influences of these parameters on the motion of the system.

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Statistical Mechanics Involving Fractal Temperature

Fractal and Fractional ◽

10.3390/fractalfract3020020 ◽

2019 ◽

Vol 3 (2) ◽

pp. 20 ◽

Cited By ~ 3

Author(s):

Alireza Khalili Golmankhaneh

Keyword(s):

Heat Capacity ◽

Partition Function ◽

Statistical Mechanics ◽

Density Of States ◽

Schrodinger Equation ◽

Time Derivative ◽

Fractional Dimension ◽

Eigenvalues And Eigenfunctions ◽

Solid Models ◽

Fractal Time

In this paper, the Schrödinger equation involving a fractal time derivative is solved and corresponding eigenvalues and eigenfunctions are given. A partition function for fractal eigenvalues is defined. For generalizing thermodynamics, fractal temperature is considered, and adapted equations are defined. As an application, we present fractal Dulong-Petit, Debye, and Einstein solid models and corresponding fractal heat capacity. Furthermore, the density of states for fractal spaces with fractional dimension is obtained. Graphs and examples are given to show details.

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Evaluation of Specific Heat Capacity and Entropy of Particle Bound Harmonics Oscillator Cosine Asymmetric Potential by Partition Function

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.886.194 ◽

2019 ◽

Vol 886 ◽

pp. 194-200

Author(s):

Piyarut Moonsri ◽

Artit Hutem

Keyword(s):

Heat Capacity ◽

Quantum Mechanics ◽

Partition Function ◽

Specific Heat ◽

Internal Energy ◽

Specific Heat Capacity ◽

Function Method ◽

Bound State ◽

State Problem ◽

Bound State Problem

In this research, a fundamental quantum mechanics and statistical mechanic bound-state problem of harmonics oscillator cosine asymmetric was considered by using partition function method. From the study, it found that the internal energy, the entropy and the specific heat capacity of particle vibration bound-state under harmonics oscillator cosine asymmetric potential were increased as the increasing of the parameters of μ, η, and β. While an increasing of parameter α affected to the decreasing of the entropy and the heat capacity. In addition, the increasing values of the entropy and the specific heat capacity value were depended on the decreasing of the parameter α value.

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