Relative-energy dependence of the Bethe-Salpeter amplitude in two-dimensional massless QED

The exact q anti q Bethe-Salpeter bound state amplitude is investigated in the space of relative energy E for a fixed value of the relative position. By means of an approximate analysis it is shown to possess singularities in E whenever one of the quarks reaches the energy threshold for the creation of a certain number of Schwinger bosons. These results are confirmed by plots of numerical results. (orig.)