Classical optics representation of the quantum mechanical translation   operator via ABCD matrices
  The ABCD matrix formalism describing paraxial propagation of optical beams across linear systems is generalized to arbitrary beam trajectories. As a by-product of this study, a one-to-one correspondence between the extended ABCD matrix formalism presented here and the quantum mechanical translation operator is established. 
Marco Ornigotti and Andrea Aiello
physics.optics