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We study the behavior of the fermion propagator in an external time dependentpotential in 0+1 dimension. We show that, when the potential has upto quadraticterms in time, the propagator can be expressed in terms of generalized Airyfunctions (or standard Airy functions depending on the exact time dependence).We study various properties of these new generalized functions which reduce tothe standard Airy functions in a particular limit.

Fermion propagator in an external potential and generalized Airy functions