  Exceptional points are special parameter points in spectra of open quantum
systems, at which resonance energies degenerate and the associated eigenvectors
coalesce. Typical examples are Rydberg systems in parallel electric and
magnetic fields, for which we solve the Schr\"odinger equation in a complete
basis to calculate the resonances and eigenvectors. Starting from an avoided
crossing within the parameter-dependent spectra and using a two-dimensional
matrix model, we develop an iterative algorithm to calculate the field
strengths and resonance energies of exceptional points and to verify their
basic properties. Additionally, we are able to visualise the wave functions of
the degenerate states. We report the existence of various exceptional points.
For the hydrogen atom these points are in an experimentally inaccessible regime
of field strengths. However, excitons in cuprous oxide in parallel electric and
magnetic fields, i. e., the corresponding hydrogen analogue in a solid state
body, provide a suitable system, where the high-field regime can be reached at
much smaller external fields and for which we propose an experiment to detect
exceptional points.
