Classical and Quantum Mechanical Aspects of Thermal Wave Physics

Abstract

In this work the therrnal wave propagation problem in generalized continuously non-homogeneous media is approached through the formal analogy that exists between classical and quantum wave fields. It is shown that the thermal wave field Hamiltonian is nondissipative irrespective of the spatial dependence of the relevant thermallthermodynamic properties of the system. The classical mechanical Hamiltonian can be shown to be that of a harmonic oscillator in the temperature potential field. Solutions to the classical mechanical problem lead to a thermal ray description which is rigorously valid only at material depths large compared to the thermal wavelength. Thermal wave propagation at any depth, however, is shown to be rigorously describable by a drastic step: quanlization of the thermal wave field Hamiltonian [8].