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CRC Press eBooks

Qualitative Methods in Quantum Theory

A.B. Migdal

Published Mar 5, 2018• 269 citations
Publisher

Abstract

This unique book, written by a leading Soviet theorist, is not a textbook of quantum mechanics but rather a compendium of the "tricks of the trade"-the methods that all practicing theoretical physicists use but few have set down in writing.
DOI
10.1201/9780429497940

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Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it could be used by senior undergraduates too.
This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive motivation for the properties of quantum mechanics, Hilbert space, and the Schrödinger equation is provided through analysis of the derivative, while standard topics like the harmonic oscillator, rotations, and the hydrogen atom are covered from within the context of operator methods. Advanced topics forming the basis of modern physics research are also included, such as the density matrix, entropy, and measures of entanglement. Written for an undergraduate audience, this book offers a unique and mathematically self-contained treatment of this hugely important topic. Students are guided gently through the text by the author's engaging writing style, with an extensive glossary provided for reference and numerous homework problems to expand and develop key concepts. Online resources for instructors include a fully worked solutions manual and lecture slides.
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