 98614 Korff C., Lang G., Schrader R.
 Twoparticle scattering for anyons
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Sep 22, 98

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Abstract. We consider potential scattering theory of a nonrelativistic quantum
mechanical 2particle system in R2 with anyon statistics. Sufficient
conditions are given which guarantee the existence of M"oller
operators and the unitarity of the Smatrix. As examples the
rotationally invariant potential well and the Deltafunction
potential are discussed in detail. In case of a general rotationally
invariant potential the angular momentum decomposition leads to a theory
of Jost functions. The anyon statistics parameter gives rise to an
interpolation for angular momenta analogous to the Regge trajectories
for complex angular momenta. Levinson's theorem is adapted to the present
context. In particular we find that in case of a zero energy resonance
the statistics parameter can be determined from the scattering phase.
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