Derivation of Admissibility Conditions for Wave Functions from General Quantum-Mechanical Principles

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Abstract
Admissibility conditions for wave functions are derived from general quantum‐mechanical principles. The conditions apply in general curvilinear coordinates to functions that describe general N‐particle systems. They restrict the behavior of wave functions so severely as to suggest that the Hilbert space of ordinary quantum mechanics cannot be enlarged unless the fundamental principles of quantum mechanics are modified. One of the conditions implies that all particles must be either fermions or bosons, i.e., that no particles obeying intermediate statistics can exist.

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