The Symmetry Character of Many-Particle Wavefunctions

Jonathan M. Selig

Huang Bao-xing

It is discussed the distributions of the wavefunction of the quantum mechanics in the classical limit, the single particle system and the ensemble of the classical mechanics. It proved that the wavefunction of the quantum mechanics can only describe an ensemble and can't describe the motion of the single particle. It is the origin of the statistical character of the quantum mechanics.

J E Gottschalk, E. N. Maslen

The few-particle Schrodinger equation does not define the symmetry of the wavefunction, which must be chosen to match the symmetry of the particles. It is shown, by reference to the S-states of a three-particle system, that the symmetry does constrain degrees of freedom associated with normalisation of the exact wavefunction. The first particle is treated as infinitely massive, and distinguishable. The systems where the second and third particles are (i) distinguishable, (ii) indistinguishable with a symmetric wavefunction (bosons) and (iii) indistinguishable with an antisymmetric wavefunction (fermions) may be treated as special cases of a continuous description of particle symmetry. Cases (ii) and (iii) are opposite extremes in the analysis.

Donald D. Fitts