A Primer on Hilbert Space Theory pdf

卡罗阿拉比索 教授在意大利米兰大学获得物理学学位，然后在意大利帕尔马的帕尔马大学任教 40 多年（期间曾在斯坦福直线加速器中心和日内瓦欧洲核子研究中心担任研究员） )，直到 2011 年退休。他的教学包括量子力学、狭义相对论、场论、基本粒子物理学、数学物理学和泛函分析等主题。 他的研究领域包括数学物理（Padé 近似）、基本粒子物理（对称性和夸克模型）和统计物理（遍历问题），并在广泛的国内和国际期刊以及之前的 Springer 书（与 Alessandro Ciesa 合着），Probledi di Meccanica Quantistica non Relativistica。

A Primer on Hilbert Space Theory pdf 卡罗阿拉比索

This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude.