Simetría y Degeneración: partícula atrapada en una caja cúbica con paredes impenetrables

Abstract

In physics as well as in chemistry the importance of symmetry is widely acknowledged. It is of common knowledge that the systems' degeneracy, in the domain of linear physical systems, is tightly related with symmetry. The stationary state degeneracy should correspond with the dimension of the symmetry group irreducible representations (irreps) associated. Therefore identifying the symmetry group is essential for labeling the energy levels. Sometimes the spectrum presents systematic accidental degeneracy, which means that the supposed symmetry group is actually a subgroup. This is the case for a particle in a cubic box, with impenetrable walls. This article presents the procedure that allows the identification of the new symmetry group that explains the degeneracy. Furthermore examples to illustrate the concepts are presented as well as the consequences implied in the selection rules.