利用球形声腔演示能级简并与对称性的关系  

Demonstrating the relationship between energy level degeneracy and symmetryusing a spherical acoustic cavity

作　　者：巩伊鸿 贾文慧 郭靖霖 白在桥[1] GONG Yi-hong;JIA Wen-hui;GUO Jing-lin;BAI Zai-qiao(Department of Physics,Beijing Normal University,Beijing 100875,China)

机构地区：[1]北京师范大学物理学系,北京100875

出　　处：《大学物理》2025年第3期100-105,共6页College Physics

摘　　要：本文研究带有长颈的球形声腔的本征频率如何随声腔对称性的破坏程度变化,旨在提供一个可以演示量子力学中对称性与能级简并之间关系的经典力学例子.在扫频信号驱动下,用麦克风采集声腔内的声压信号,根据功率谱得到声腔的本征频率.对l=2的情况,当SO(3)对称性破坏但保留SO(2)对称性时,实验发现原本简并的3个本征频率分裂成2个.当进一步破坏SO(2)对称性仅保留离散的反射对称性时,3个本征频率完全分开.利用COMSOL Multiphysics数值模拟,验证了实验现象,同时指出了实验中发现的某些本征频率对扰动不敏感的原因:这些态的本征模式具有奇宇称,在瓶颈附近的振幅很小.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.

关 键 词：对称性 本征频率 简并 塞曼效应 LABVIEW COMSOL 

分 类 号：O424[理学—声学]