关键词: 对称性, 本征频率, 简并, 塞曼效应, LabVIEW, COMSOL

Abstract: We use an empty glass shell with a long neck and study how its eigenfrequency splits after breaking the symmetry. Our goal is to provide an example to show the relation between symmetry and energy degeneracy in quantum mechanics. The system is driven by a swept signal, and we use a microphone to acquire acoustic signals in the glass shell. Then we derive the eigenfrequencies of the shell from the power spectrum. For l=2, if we break the SO(3) symmetry while keeping the SO(2) symmetry, according to experiment, the initial degenerate three eigenfrequencies exhibit into two eigenfrequencies, one of which has two-fold degeneracy. When we continue to break its SO(2) symmetry and keep its discrete reflectional symmetry only, the three eigenfrequencies separate completely. We simulate this progress by applying COMSOL Multiphysics and find the reasons that some eigenfrequencies are insensitive to perturbations in the experiment: these states are odd and have small amplitudes near the neck of the shell.

Key words: symmetry, eigenfrequency, degeneracy, Zeeman effect, LabVIEW, COMSOL