Accidental degeneracies in quantum mechanics and the symmetries of the classical Hamiltonian

Dahyeon Lee

S. P. Alliluev

Dieter Schuch

G B Shaw

The notions of systematic and accidental degeneracy are discussed for a quantum-mechanical particle in a two-dimensional box. Separability of coordinates is shown to admit extra systematic degeneracy over that expected from the point-group symmetry. The 'accidental' degeneracy for square and triangular boxes is discussed in detail and related to geometric symmetries-described by rings of operators, however, and not by a symmetry group.

J. M. Jauch, Edward L. Hill

Harold V. McIntosh

The theory of accidental degeneracy is surveyed, particular attention being paid to the connection between the accidental degeneracy of the two-dimensional isotropic harmonic oscillator and the theory of angular momentum.