Difficulty and Possibility of Kinetic Theory of Quantum-Mechanical Systems. Part V. Particular and General Solutions of the Schrodinger Equation and Their Significance in Kinetic Theory

摘要

The quantum-mechanical Liouville equation is more restrictive and hence more informative than the Schrodinger equation, because the former already contains the definition of independent variable p, momentum in a special case. In this sense, the quantum-mechanical Liouville equation is more definitive as the description of a physical law, and is shown to be invariant under the Galilean transformation. By taking advantage of this convenience, the author obtains a particular solution of the Schrodinger equation for n-particle system. This solution is localized in the phase space and stable in time, and seems to represent an n-particle system as single system. The de Broglie wave is constructed by superposing a number of similar particular solutions for single-particle systems. Similarly, general solution is constructed for n-particle systems. For justification of its application to kinetic theory, Pauli's principle is analyzed and interpreted anew. The present solution promises the possibility of rational methods of kinetic theory of quantum-mechanical systems, as analogous to methods of classical kinetic theory. (Author)