Quantum impulse control
The quantum adiabatic theorem governs the evolution of a wavefunction under a slowly time-varying Hamiltonian. I will consider the opposite limit of a Hamiltonian that is varied impulsively: an infinitely strong perturbation U(x,t) is applied over an infinitesimal time interval. When the strength and duration of the perturbation scale appropriately, the impulse causes the wavefunction y(x,t) to undergo a sudden displacement and/or deformation. Remarkably, this evolution is described by a purely classical construction. I will use these results to show how tailored impulses can be used to control the behavior of a quantum wavefunction, in one or more degrees of freedom.