In quantum mechanics, calculations (at least formally) boil down to the diagonalization of Hermitian matrices - in particular, the Hamiltonian, or in the continuous case, the solution of linear differential equations. Again, observed degeneracies in the eigenspectrum are a consequence of discrete (or continuous) symmetries. In the latter case, Noether's theorem also guarantees a conserved current. "Accidental" symmetry is the name given to observed degeneracies that are apparently not a consequence of symmetry.