Ground State Wave Function of the Schr\"odinger Equation in a   Time-Periodic Potential
  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. 
Stefano Galluccio and Yi-Cheng Zhang (Institut de Physique The'orique,   Universite' de Fribourg, Switzerland)