Quantum Theory of Atoms
The fact that both l and m are restricted to certain values is due to boundary conditions
in the figure, l=2 is shown
hence L=(2(2+1))1/2 h = h(6)1/2
the Schrödinger equation can be solved exactly for hydrogen
the energies are the same as in the Bohr theory En = -Z2 (13.6 eV)/n2
they do not depend on the value of l and m
this is a special property of an inverse-square law force