Thermodynamics of the two-dimensional quantum harmonic oscillator system subject to a hard-wall confining potential

Abstract

We study a two-dimensional isotropic harmonic oscillator with a hard-wall confining potential in the form of a circular cavity defined by the radial coordinate ρ0. When one can normalise the wave function by obtaining polynomial solutions and, in this way, the discrete energy spectrum of the system in an analytical closed form. On the other hand, for , the radial coordinate becomes defined in the range 0 < ρ < ρ0 and the energy spectrum can only be numerically obtained. The thermodynamics of the system can nevertheless be computed and the results compared to the well-studied free oscillator. For instance, the specific heat of the confined oscillator presents a peak and the corresponding limiting value at high temperatures deviates from the expected Dulong–Petit law value. In addition, there is a particular limiting case where a discrete spectrum of energy of the confined oscillator can be obtained in an analytical form. In this case, not only the energy spectrum but also its thermodynamics are comparable to the exact results, even for rather large values of the cavity size.

Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space–time

“…This fact is consistent with a statement in Ref. [91] for harmonic oscillators with a hard-wall confinement. However, it suffices that the amplitude of the wave function be negligibly small at distances larger than the hardwall.…”

“…in Ref. [91], hereafter we express the validity of our solution with Heun polynomials in terms of the physical parameters required to obtain the desired statistical significance [92]. The statistical significance quantifies by how much the probability of our wave function lies outside the hard-wall.…”

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“…For example, Chargui and Dhahbi [41] investigated the statistical properties of a two-dimensional Dirac oscillator (2D DO) in the presence of a spin-orbit coupling, breaking its supersymmetry. The high temperature limit of different thermodynamical functions was probed analytically by utilizing the Euler-Maclaurin formula.Valentim et al [42] studied a two-dimensional isotropic harmonic oscillator with a hard-wall confining potential in the form of a circular cavity defined by the radial coordinate 0  . The thermodynamics properties of the system was computed and the results compared to the well-studied free oscillator.…”