Mathematical Sciences: Semi-Classical Analysis and Geometric Quantization

9623054 Uribe提出的研究属于数学物理的一般领域。更具体地说，研究者打算研究经典力学中的约简过程与量子力学中相应的运算之间的关系，即在对称性下相关希尔伯特空间对向量不变量空间的限制。紧黎曼流形上薛定谔型算子的特征函数的几何性质也将在半经典极限下进行研究。提出的工作源于量子力学中出现的各种数学难题；在于现代分析与几何的结合。量子力学虽然比经典力学做出更准确的预测，但被该领域的一些工作者认为存在着某些基础和技术上的困难，其中最重要的是涉及到非常困难的数学。

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.