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We find the full spectrum of fermion bound states on a Z_2 kink. In additionto the zero mode, there are int[2 m_f/m_s] bound states, where m_f is thefermion and m_s the scalar mass. We also study fermion modes on the backgroundof a well-separated kink-antikink pair. Using a variational argument, we provethat there is at least one bound state in this background, and that the energyof this bound state goes to zero with increasing kink-antikink separation, 2L,and faster than e^{-a2L} where a = min(m_s, 2 m_f). By numerical evaluation, wefind some of the low lying bound states explicitly.

Fermions on one or fewer Kinks