Working Paper Article Version 1 This version is not peer-reviewed

Classical Linear Harmonic Oscillators to Describe Thermodynamic Properties of Quantum Linear Harmonic Oscillators and Solids

Version 1 : Received: 17 June 2019 / Approved: 19 June 2019 / Online: 19 June 2019 (08:06:19 CEST)

How to cite: Umirzakov, I.H. Classical Linear Harmonic Oscillators to Describe Thermodynamic Properties of Quantum Linear Harmonic Oscillators and Solids. Preprints 2019, 2019060180 Umirzakov, I.H. Classical Linear Harmonic Oscillators to Describe Thermodynamic Properties of Quantum Linear Harmonic Oscillators and Solids. Preprints 2019, 2019060180

Abstract

As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature dependent masses or (and) frequencies has the same partition function as the system consisting of quantum linear harmonic oscillators having temperature independent masses and frequencies while the means of the square displacements of the positions of the oscillators from their mean positions for the system consisting of classical linear harmonic oscillators having: the temperature dependent masses; temperature dependent frequencies; and temperature dependent masses and frequencies differ from each other and from that of the system consisting of quantum linear harmonic oscillators, and hence, the system consisting of classical linear harmonic oscillators describes well the thermodynamic properties of the system consisting of quantum linear harmonic oscillators and solids.

Subject Areas

solids; quantum linear harmonic oscillator; classical linear oscillator; partition function; Hamiltonian; position fluctuations; Hamilton function; thermodynamic properties

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