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Applied Mechanics and Materials

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

Piyarut Moonsri, Artit Hutem

Published Jan 1, 2019• 0 citations
Publisher

Abstract

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.

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

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The thermostatistic properties of a q-generalized boson system trapped in an n-dimensional harmonic oscillator potential are studied, based on the generalized statistic distribution derived from Tsallis' entropy. The density of states, total number of particles, critical temperature at which Bose-Einstein condensation occurs, internal energy, and heat capacity at constant volume are derived. The characteristics of Bose-Einstein condensation of the system are discussed in detail. It is found from the results obtained here that the thermostatistic properties of such a system depend closely on parameter q, dimensional number of the space, and frequency of the harmonic oscillator; and the external potential has a great influence on the thermostatistic properties of the system.
Abstract The exact solutions of a one‐dimensional Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained. The ladder operators constructed directly from the normalized wavefunctions are found to satisfy a su(1, 1) algebra. Another hidden symmetry is used to explore the relations between the eigenvalues and eigenfunctions by substituting x → −ix. The vibrational partition function Z is calculated exactly to study thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F, and entropy S. It is both interesting and surprising to find that both vibrational specific heat C and entropy S are independent of the potential strength α. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
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The density matrix in the position and momentum representation, the position-momentum uncertainty product, the Wigner and Q functions, and thermal properties of the family of the nonclassical maximum-entropy states of a single harmonic oscillator are determined. Any such state, having the mean number of quanta n , has the uncertainty product x p = (2 n +1)( /2), and this product attains its minimum value for the temperature parameter 0. Generically, the Wigner function has alternating sign so that the underlying maximum-entropy state is truly nonclassical. The von Neumann entropy and the heat capacity, expressed via the temperature parameter , coincide with the corresponding quantities for the thermal state. The properties discussed here are of interest for the description and analysis of the vibrational motion of a trapped ion in a harmonic-oscillator potential since the equilibrium states which result under certain conditions are the maximum-entropy states.