  We explore the method of old quantization as applied to states with nonzero
angular momentum, and show that it leads to qualitatively and quantitatively
useful information about systems with spherically symmetric potentials. We
begin by reviewing the traditional application of this model to hydrogen, and
discuss the way Einstein-Brillouin-Keller quantization resolves a mismatch
between old quantization states and true quantum mechanical states. We then
analyze systems with logarithmic and Yukawa potentials, and compare the results
of old quantization to those from solving Schrodinger's equation. We show that
the old quantization techniques provide insight into the spread of energy
levels associated with a given principal quantum number, as well as giving
quantitatively accurate approximations for the energies. Analyzing systems in
this manner involves an educationally valuable synthesis of multiple numerical
methods, as well as providing deeper insight into the connections between
classical and quantum mechanical physics.
