Colóquio: Thermodynamics of the two-dimensional quantum harmonic oscillator system subject to a hard-wall confining potential (João Antônio Plascak)

Ciclo de Colóquios

Colóquio #1

01/09/2023, 16h00

https://meet.google.com/kzv-piom-bey

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

Prof. Dr. João Antônio Plascak

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 ρ0 goes to infinity 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 ρ0 finite, the radial coordinate becomes defined in the range 0<ρ

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 ρ0 goes to infinity 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 ρ0 finite, 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.