Quantum Theory for Mathematicians
數(shù)學(xué)家的量子理論

Author：Brian C. Hall



Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics.
盡管量子物理的思想在現(xiàn)代數(shù)學(xué)的許多部分中扮演著重要的角色，但是很少有針對(duì)數(shù)學(xué)家的關(guān)于量子力學(xué)的書籍。這本書用數(shù)學(xué)家熟悉的語言介紹了量子力學(xué)的主要思想。以前很少接觸物理的讀者會(huì)喜歡這本書的對(duì)話基調(diào)，因?yàn)樗麄兩钊胙芯恐T如希爾伯特空間量子理論的方法；一維空間中的薛定諤方程；有界和無界自伴算子的譜定理；斯通-馮-諾依曼定理；溫澤爾-克萊默斯-布里淵近似；李群和李代數(shù)在量子力學(xué)中的作用；量子力學(xué)的路徑積分方法。

The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
每章結(jié)尾的大量練習(xí)使這本書既適合研究生課程，也適合獨(dú)立學(xué)習(xí)。大部分的課文對(duì)數(shù)學(xué)研究生來說都是可以訪問的，他們?cè)谡鎸?shí)分析中有第一門課程，包括第二語言空間和希爾伯特空間的基礎(chǔ)知識(shí)。最后幾章向熟悉流形理論的讀者介紹更高級(jí)的主題，包括幾何量子化。

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