  We discuss the properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap
being commonly used in ultracold atomic physics experiments. The Hamiltonian is
derived and it is demonstrated how tight traps alter the coupling of the atom
to the magnetic field. We solve the underlying Schroedinger equation of the
system within a given n-manifold and show that for a sufficiently large Ioffe
field strength the 2n^2-dimensional system of coupled Schroedinger equations
decays into several decoupled multicomponent equations governing the center of
mass motion. An analysis of the fully quantized center of mass and electronic
states is undertaken. In particular, we discuss the situation of tight center
of mass confinement outlining the procedure to generate a low-dimensional
ultracold Rydberg gas.
