Hydrogen (Coulomb potential) radial equation
is solved by finding the behavior at large
then finding the behavior at small
then using a power series solution to get
So a Hydrogen energy eigenstate is described by three integer quantum numbers with the requirements that , and also an integer, and . The ground state of Hydrogen is and has energy of -13.6 eV. We compute several of the lowest energy eigenstates.
The diagram below shows the lowest energy bound states of Hydrogen and their typical decays.
Jim Branson 2013-04-22