Hidden antiunitary symmetry behind “accidental” degeneracy and its protection of degeneracy
Jing-Min Hou1(), Wei Chen2
1. School of Physics, Southeast University, Nanjing 211189, China 2. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
In quantum mechanics, accidental degeneracy refers to energy degeneracy that occurs coincidentally, without any protection by symmetry. Here, we prove a theorem stating that any two-fold degeneracy (accidental or not) in a quantum system is protected by a novel hidden symmetry, which can be expressed by an antiunitary operator with its square being −1. In this sense, the so-called accidental degeneracy is not really accidental, and this actually implies a hidden antiunitary symmetry.
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