  As a contribution to quantum optics in the vicinity of surfaces we study the
single atom spontaneous emission in a linear chain of two-level atoms. The
electromagnetic field is thereby treated with the help of integro-differential
equations which take into account the interaction with the other atoms in the
chain. The life time of the excited atom, the frequency shift of the atomic
transition and the angular distribution of emitted photons are worked out. They
depend on the position of the emitting atom. As compared with the single atom
in free space, considerable modifications occur for atoms a few interatomic
distances away from the ends of the chain.
