A general kinetic theory of liquids. IV. Quantum mechanics of fluids

Abstract

In this paper the classical theory of liquids developed in the first three parts of this series is translated into the quantum formalism. After the fundamental equations have been reformulated, it is shown that in the classical limit $\hslash $ = 0, they go over into the corresponding classical equations. A quantized proof of the Boltzmann distribution law is given which is simpler and more direct than that of the Darwin-Fowler method. Then the equation of state is derived in a form which exhibits clearly the deviations from the classical law at very low temperatures. An approximate method of solution of the fundamental equations is developed in a form suitable for practical application. Finally, the quantum equations of motion and energy transport are obtained, and it is shown that they are formally identical with the classical 'hydrodynamical equations'. This enables a discussion of the viscosity and thermal conductivity of quantum liquids to be given which exposes clearly the alternative explanations of the abnormal properties of liquid He II.