Mathematical Sciences: Semi-Classical Analysis and Geometric Quantization

9623054乌里韦拟议的研究涉及数学物理的一般领域。更具体地说，作者打算研究经典力学中的约化过程与量子力学中的相应运算之间的关系，即结合的希尔伯特空间对对称下不变的矢量空间的限制。在半经典极限下，还将研究紧致黎曼流形上薛定谔算子的本征函数的几何。这项拟议的工作源于量子力学带来的各种数学困难；存在于现代分析和几何之间的接口。尽管量子力学做出了比经典力学更准确的预测，但该领域的一些工作者认为，量子力学面临着某些基础和技术上的困难，其中最重要的是涉及的非常困难的数学问题。

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.