Mathematical Sciences: Semi-Classical Analysis and Geometric Quantization

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9623054 Uribe The proposed research lies in the general area of mathematical physics. More specifically, the investigator intends to study the relationship between the reduction procedure in classical mechanics and the corresponding operation in quantum mechanics, namely the restriction of the associated Hilbert space to the space of vectors invariant under the symmetries. The geometry of eigenfunctions of a Schrodinger-type operator on a compact Riemannian manifold will also be studied, in the semi-classical limit. The proposed work stems from various mathematical difficulties coming out of quantum mechanics; lies in the interface between modern analysis and geometry. Quantum mechanics, although makes more accurate predictions than classical mechanics, is perceived to be riddled with certain foundational as well as technical difficulties by some workers in the field, not the least among these difficulties are the very difficult mathematics involved.