Quantum Theory for Mathematicians
数学家的量子理论

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.
尽管量子物理的思想在现代数学的许多部分中扮演着重要的角色，但是很少有针对数学家的关于量子力学的书籍。这本书用数学家熟悉的语言介绍了量子力学的主要思想。以前很少接触物理的读者会喜欢这本书的对话基调，因为他们深入研究诸如希尔伯特空间量子理论的方法；一维空间中的薛定谔方程；有界和无界自伴算子的谱定理；斯通-冯-诺依曼定理；温泽尔-克莱默斯-布里渊近似；李群和李代数在量子力学中的作用；量子力学的路径积分方法。

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.
每章结尾的大量练习使这本书既适合研究生课程，也适合独立学习。大部分的课文对数学研究生来说都是可以访问的，他们在真实分析中有第一门课程，包括第二语言空间和希尔伯特空间的基础知识。最后几章向熟悉流形理论的读者介绍更高级的主题，包括几何量子化。

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