This accidental degeneracies are known as diabolic points.
2.
An accidental degeneracy can be due to the fact that the group of the Hamiltonian is not complete.
3.
For a particle in a central 1 / r potential, the Laplace Runge Lenz vector is a conserved quantity resulting from an accidental degeneracy, in addition to the conservation of angular momentum due to rotational invariance.
4.
The degeneracy with respect to l is often described as an accidental degeneracy, but it can be explained in terms of special symmetries of the Schr�dinger equation which are only valid for the hydrogen atom in which the potential energy is given by Coulomb's law.
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