  Using a generalized transfer matrix method we exactly solve the Schr\"odinger
equation in a time periodic potential, with discretized Euclidean space-time.
The ground state wave function propagates in space and time with an oscillating
soliton-like wave packet and the wave front is wedge shaped. In a statistical
mechanics framework our solution represents the partition sum of a directed
polymer subjected to a potential layer with alternating (attractive and
repulsive) pinning centers.
