Symmetry group of a particle in an impenetrable cubic well potential

8th International Symposium on Quantum Theory and Symmetries

Hernández-Castillo, A.O.^1 ; Lemus, R.^1

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de Mexico, A. P. 70-543, Circuito Exterior, C. U., D.F., Mexico 04510, Mexico^1

关键词: A-particles;    Irreducible representations;    Linear combinations;    OH group;    Quantum particles;    Semidirect product;    Symmetry groups;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/512/1/012025/pdf
DOI  :  10.1088/1742-6596/512/1/012025

来源: IOP

【 摘 要 】

A quantum particle in a impenetrable cubic well potential presents accidental degeneracy when the Oh group is considered to be the symmetry group of the system. This degeneracy becomes natural when a new symmetry group, embedding the Ohgroup, is proposed. This new group turns out to be the semidirect product G = TOh, where T is a two-dimensional compact continuous group whose generators correspond to linear combinations of the onedimensional 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.