In order to keep the wavefunction finite at infinity the power series defining must terminate. For a given l the possible values of E kl then are . In terms of c 0 the various coefficients c q are calculated using the recurrence relations . . . The associate Laguerre polynomials are defined as . We therefore have .
Normalization requires . .
We therefore have . . This is the essential degeneracy, since E kl does not depend on m . Accidental degeneracies also exist. The possible eigenenergies therefore are . Here n is called the principal quantum number , n fixes the energy of the eigenstate.