A Mathematical Companion to Quantum Mechanics

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.

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.

Introduction
The Fourier transform
The spectral theorem, I
Unbounded operators
Semi-groups, I
Self-adjoint operators
Semi-groups, II
Semi-groups, III
Weyl's theorem on the essential spectrum
More from Weyl's theorem
Extending the functional analysis via Riesz
Wintner's proof of the spectral theorem
The L2 version of a spectral theorem
Rayleigh-Ritz
Some one-dimensional quantum mechanics
More one-dimensional quantum mechanics
Some three-dimensional computations
Bound states and scattering states
The exponential decay of eigenstates
Lorch's proof of the spectral theorem
Scattering theory via Lax and Phillips
Huygens' principle
Some quantum mechanical scattering theory
The Groenwald-van Hove theorem
Chernoff's theorem
Some background material