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Sternberg S. A Mathematical Companion to Quantum Mechanics

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New York, USA: Dover Publications, Inc., 2019. — 336 p. — ISBN 0486826899.
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.
Table of Contents
Introduction
The Fourier Transform
The Spectral Theorem
Unbounded Operators
Semi-groups, I
Self-adjoint Operators
Semi-groups, II
Semi-groups, III
Weylв’s Theorem on the Essential Spectrum
More from Weylв’s Theorem
Extending the Functional Analysis via Riesz
Wintnerв’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
States and Scattering States
Exponential Decay of Eigenstates
Proof of the Spectral Theorem
Theory via Lax and Phillips
Principle
Quantum Mechanical Scattering Theory
Groenewold-van Hove Theorem
Theorem
Background Material
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