Wigner quantum oscillators. Osp(3/2) oscillators

TL;DR

This paper explores the properties of osp(3/2) quantum oscillators, revealing their unique angular momentum, anticommuting coordinates, and diverse energy spectra, which differ from canonical oscillators and include degenerate ground states.

Contribution

It provides a detailed analysis of the noncanonical osp(3/2) oscillators, highlighting their angular momentum structure, anticommutation relations, and spectral characteristics.

Findings

Angular momentum M takes values p-1, p, p+1, all integers or all half-integers.

Coordinates anticommute with each other.

Energy spectrum varies and can differ significantly from canonical oscillators.

Abstract

The properties of the three-dimensional noncanonical osp(3/2) oscillators, introduced in J.Phys. A: Math. Gen. {\bf 27} (1994) 977, are further studied. The angular momentum M of the oscillators can take at most three values M=p-1,p,p+1, which are either all integers or all half-integers. The coordinates anticommute with each other. Depending on the state space the energy spectrum can coincide or can be essentially different from those of the canonical oscillator. The ground state is in general degenerated.