The
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

with . To keep the wavefunction normalizable the power series must terminate, giving us our

Here is called the

where is the number of nodes in the radial wavefunction. It is an odd feature of Hydrogen that a radial excitation and an angular excitation have the same energy.

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