Supersymmetry solution for finitely extensible dumbbell model

Exact relaxation times and eigenfunctions for a simple mechanical model of polymer dynamics are obtained using supersymmetry methods of quantum mechan ics. The model includes the finite extensibility of the molecule and does n ot make use of the selfconsistently averaging approximation. The finite ext ensibility reduces the relaxation times when compared to a linear force. Th e linear viscoelastic behaviour is obtained in the form of the "generalized Maxwell model". Using these results, a numerical integration scheme is pro posed in the presence of a given flow kinematics.