Mathematical Sciences: Singular Perturbations, Oscillatory Integrals, and Point Interactions

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Professor Hughes will apply work of Ricci and Stein on oscillatory integrals to singular perturbation problems arising in quantum mechanics. In addition Hughes will consider the solution of the time dependent Schroedinger equation with singular time dependent interactions. A unifying theme will be the use of the interaction representation for solutions of the Schroedinger equation. This work involves the mathematics of quantum mechanics. Professor Hughes will apply new mathematical techniques to understand the behavior of interacting quantum mechanical particles.