Symmetry group of a particle in an impenetrable cubic well potential

摘要

A quantum particle in a impenetrable cubic well potential presents accidental degeneracy when the O_h group is considered to be the symmetry group of the system. This degeneracy becomes natural when a new symmetry group, embedding the O_h group, is proposed. This new group turns out to be the semidirect product g = T∧O_h, where T is a two-dimensional compact continuous group whose generators correspond to linear combinations of the one-dimensional Hamiltonians. The systematic degeneracy is studied in detail, the new group is identified and its irreducible representations (irreps) are constructed by means of induction, an approach that allows the irreducibility and completeness to be assured. Pythagorean degeneracy as well as the one due to commensurable sides are not considered.