  The electronic spectrum of a Rydberg atom immersed in a Bose-Einstein
condensate is investigated. The Heisenberg equations of motions for the
condensate and the Rydberg atom are derived. Neglecting the backaction of the
Rydberg atom onto the condensate decouples the equations describing the
condensate and Rydberg atom. In this case the spectral structure of the Rydberg
atom is completely determined by an effective potential which depends on the
density distribution of the condensate. We study the spectral properties for
the situation of an isotropic harmonic and anharmonic as well as axially
symmetric confinement. In the latter case an intriguing analogy with Rydberg
atoms in magnetic fields is encountered.
