  In addition to the well known case of spherical coordinates the hydrogen atom
separates in three further coordinate systems. Separating in a particular
coordinate system defines a system of three commuting operators. We show that
the joint spectrum of the Hamilton operator, and the $z$-components of the
angular momentum and quantum Laplace-Runge-Lenz vectors obtained from
separation in prolate spheroidal coordinates has quantum monodromy for energies
sufficiently close to the ionization threshold. This means that one cannot
globally assign quantum numbers to the joint spectrum. Whereas the principal
quantum number $n$ and the magnetic quantum number $m$ correspond to the
Bohr-Sommerfeld quantization of globally defined classical actions a third
quantum number cannot be globally defined because the third action is globally
multi valued.
