Thermodynamic properties and algebraic solution of the N-dimensional harmonic oscillator with minimal length uncertainty relations

Uncertainty relations for the time-dependent singular oscillator in the number state and in the coherent state are investigated. We applied our developement to the Caldirola–Kanai oscillator perturbed by a singularity. For this system, the variation (Δx) decreased exponentially while (Δp) increased exponentially with time both in the number and in the coherent states. As k → 0 and χ → 0, the number state uncertainty relation in the ground state becomes 0.583216ℏ which is somewhat larger than that of the standard harmonic oscillator, ℏ/2. On the other hand, the uncertainty relation in all excited states become smaller than that of the standard harmonic oscillator with the same quantum number n. However, as k → ∞ and χ → 0, the uncertainty relations of the system approach the uncertainty relations of the standard harmonic oscillator, (n+1/2)ℏ.

Download Full-text

Statistical aspects of harmonic oscillator under minimal length supposition

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2015.01.041 ◽

2015 ◽

Vol 425 ◽

pp. 10-17 ◽

Cited By ~ 8

Author(s):

L. Farhang Matin ◽

S. Miraboutalebi

Keyword(s):

Harmonic Oscillator ◽

Minimal Length

Download Full-text

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.

Download Full-text