If a polynomial has multiple roots, we may modify its coefficients a little bit so that
all its roots become simple. Similarly, for the Schrödinger
equation, we may perturb the Hamiltonian operator a little bit and remove the
degeneracy of its eigenvalues.
First excited states of helium
The reason for the removal of the l degeneracy [Lev2, p.271, l.-16-l.-3].
The reason for the removal of the exchange degeneracy [Lev2, p.271, l.-2-p.272, l.11].