Three-body S-state wavefunctions: symmetry and degrees of freedom associated with normalisation of the exact wavefunction

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Abstract
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.