  We study hydrogen-like atoms in N=1 supersymmetric quantum electrodynamics
with an electronic and a muonic family. These atoms are bound states of an
anti-muon and an electron or their superpartners. The exchange of a photino
converts different bound states into each other. We determine the energy
eigenstates and calculate the spectrum to fourth order in the fine structure
constant. A difference between these perfect atoms and non-supersymmetric ones
is the absence of hyperfine structure. We organize the eigenstates into super
multiplets of the underlying symmetry algebra.
