As definition suggests accidental degeneracy is defined by the degeneracy generated by two symmetry protected states. But how is it different from a non accidental degeneracy.

  • $\begingroup$ If the multiplicity of a state is 1 then if its energy is the same as another state this is accidental, for example the energy of 3 quanta of vibration 1 may be the same as 2 quanta of vibration 2, unlikely but possible. If the multiplicity is greater than 1 the levels are properly degenerate, e.g. doublet, triplet states, provided no perturbation splits them, e.g. a magnetic field. (btw. I don't understand what you mean by 'symmetry protected') $\endgroup$ – porphyrin Jul 30 '20 at 15:58

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