CHAPTER 6 - IDENTITY OF PARTICLES

Abstract

This chapter discusses the principle of indistinguishability of similar particles, Exchange interaction, and the case of Fermi statistics. In quantum mechanics, there is in principle no possibility of separately following each of a number of similar particles and thereby distinguishing them. One may say that, in quantum mechanics, identical particles entirely lose their “individuality.” The identity of the particles with respect to their physical properties is very far-reaching: it results in the complete indistinguishability of the particles. This principle of the indistinguishability of similar particles, as it is called, plays a fundamental part in the quantum theory of systems composed of identical particles. The wave function of identical particles must either be unchanged when any pair of particles are interchanged and hence when the particles are permuted in any manner, or change sign when any pair are interchanged. In the first case, the chapter discusses a symmetrical wave function, and in the second case of an antisymmetrical one. The property of being described by symmetrical or antisymmetrical wave functions depends on the nature of the particles. Particles described by antisymmetrical functions are said to obey Fermi-Dirac statistics (or to be fermions), while those which are described by symmetrical functions are said to obey Bose-Einstein statistics (or to be bosons).