Demonstration of the Spin-Statistics Connection in Elementary Quantum Mechanics

Abstract

A simple demonstration of the spin-statistics connection is presented. The effect of exchange and space inversion operators on two-particle states is reviewed. The connection follows directly from successive application of these operations to the two-particle wave function for identical particles in an s-state, evaluated at spatial coordinates ±x, but at equal time, i.e., at spacelike interval.

Connecting Spin and Statistics in Quantum Mechanics

“…Closest to the present approach are those papers that use only quantum mechanics, relativistic or nonrelativistic, and are written in the spirit of Feynman's demand for simplicity. These papers nevertheless contain one or several of the following restrictions: the wave functions must have special invariance [11,12], continuity [13][14][15][16][17] or symmetry [18] properties, or must lie in special spin-component subspaces [19]. The systems considered must be nonrelativistic [13][14][15][16][17][18][19][20][21][22], have only two spatial dimensions [22], contain only two particles [18,19], only particles with zero spin [13][14][15][16][17] or spin ≤ 1/2 [20,21], only point particles [23][24][25], must admit antiparticles [26], or the exchange must be considered as physical transportation of real objects [11,12,[23][24][25]27].…”