Carlo Alabiso,Ittay Weiss
A Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups
A Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups
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Excellent- More about A Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups
This book provides an essential introduction to Hilbert space theory, a fundamental tool for non-relativistic quantum mechanics, in a rigorous but reader-friendly fashion. It is ideal for use in upper undergraduate and lower graduate courses in Physics and Mathematics.
Format: Paperback / softback
Length: 328 pages
Publication date: 05 March 2022
Publisher: Springer Nature Switzerland AG
This comprehensive book provides an essential introduction to the theory of Hilbert space, a fundamental tool in non-relativistic quantum mechanics. It delves into linear, topological, metric, and normed spaces, presenting them in a rigorous yet accessible manner. The rationale behind offering an introduction to Hilbert space rather than a detailed study lies in the mathematical complexities inherent in even the simplest physical cases. Graduate courses in physics often struggle to cover the theory of Hilbert space and operators, distribution theory, and other mathematical topics with sufficient rigor. Consequently, compromises must be made between mathematical precision and practical application.
Based on the author's lectures on functional analysis for graduate students in physics, this book aims to equip readers with a more practical approach to Hilbert space and its applications. It includes a brief introduction to topological groups and other mathematical structures akin to Hilbert space. The main text is accompanied by exercises and solved problems, allowing readers to deepen their understanding. The topics and their presentation have been carefully curated to expedite the learning process while maintaining rigorous and effective preparation for the intricacies of Hilbert space.
The book is particularly well-suited for use in upper undergraduate and lower graduate courses in Physics and Mathematics. Its comprehensive coverage and clear explanations make it an invaluable resource for students seeking to grasp the fundamentals of Hilbert space and its applications in modern physics.
Weight: 539g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030674199
Edition number: 2nd ed. 2021
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