Shlomo Sternberg

A Mathematical Companion to Quantum Mechanics (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Guilford Publications
• Seitenzahl: 336
• Erscheinungstermin: 20. März 2019
• Englisch
• ISBN-13: 9780486839820
• Artikelnr.: 56248787

Autorenporträt

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.

Inhaltsangabe

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