A Mathematical Companion to Quantum Mechanics (Paperback)

This original 2019 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students studying quantum mechanics. Its intended audience is students of mathematics at the senor university level and beginning graduate students in mathematics and physics.
Early chapters address such topics as the Fourier transform, the spectral theorem for bounded self-joint operators, and unbounded operators and semigroups. Subsequent topics include a discussion of Weyl's theorem on the essential spectrum and some of its applications, the Rayleigh-Ritz method, one-dimensional quantum mechanics, Ruelle's theorem, scattering theory, Huygens' principle, and many other subjects.

這本原創於2019年的著作，基於作者在哈佛大學多年的教學經驗，探討了對於高年級本科生和研究生學習量子力學的數學方法。它的目標讀者是高年級大學數學學生和初級研究生數學和物理學生。

早期章節涵蓋了傅立葉變換、有界自共軛算子的譜定理，以及無界算子和半群。隨後的主題包括了對韋伊爾定理及其應用的討論、瑞利-里茲方法、一維量子力學、魯埃爾定理、散射理論、惠更斯原理等等。

Shlomo Sternberg received his Ph.D. from Johns Hopkins University in 1957 and taught in the Mathematics Department at Harvard University from 1959 until his retirement as Professor Emeritus of Mathematics in 2017. He is the author of many frequently cited and highly regarded books in mathematics and related fields, including two published by Dover: Dynamical Systems and Curvature in Mathematics and Physics. Among many other honors and awards, Dr. Sternberg was elected to the American Academy of Arts and Sciences in 1984 and to the National Academy of Sciences in 1986.

Shlomo Sternberg於1957年從約翰霍普金斯大學獲得博士學位，並於1959年至2017年期間在哈佛大學數學系擔任教職，退休時為數學名譽教授。他是數學和相關領域中許多被引用和高度評價的書籍的作者，其中包括兩本由Dover出版的書籍：《動力系統》和《數學和物理中的曲率》。Sternberg博士還獲得了許多其他榮譽和獎項，包括1984年當選為美國藝術與科學學院院士和1986年當選為美國國家科學院院士。