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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