Elementary Theory of Quantum-Mechanical Collective Motion of Particles, I

Abstract

An elementary theory of quantum-mechnaical collective motion of many-particle systems is developed. The fundamental idea is illustrated by taking an example of surface oscillation of an incompressible system of particles. The essential point of the theory is, roughly speaking, the neglect of 1/√N against unity, N being the number of particles of the system. The method is a natural generalization of separation of translational motion from the internal relative motion by the use of centre of mass coordinates. A description in terms of field concept is briefly discussed.