---
product_id: 40310741
title: "Mathematics of Classical and Quantum Physics (Dover Books on Physics)"
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# Mathematics of Classical and Quantum Physics (Dover Books on Physics)

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Review: A Masterpiece - This book is nothing short of a mathematical symphony! One of the best books on the subject of Hilbert Spaces and Inner Product Spaces (in addition to Fourier series and transform). The subject of inner product spaces is a subtle one and the authors do a superb job in developing it piece by piece in the most elegant way I've seen (so far). Chapters 3, 4, and 5 are devoted to the development of the subjects of inner product spaces, Hilbert Spaces, and related concepts such as Linear Transformations, Eigenvalues and Eigenvectors, and Orthogonality and Completeness. For a physics student, the materials in the these three chapters is all they'd need to manage through a Quantum Mechanics course at the level of both Griffiths' Introduction to Quantum Mechanics and Shankar's Principles of Quantum Mechanics and similar books (such as my favorite book on quantum mechanics: A Modern Approach to Quantum Mechanics by John Townsend). All the polynomials such Hermite, Legendre, and Laguerre polynomials which are necessary to understand the derivations of the various eigen-functions in QM are nicely developed early on in the book. I should also mention that the first two chapters of the book dealing with mathematics of Classical Mechanics are also extremely useful. Chapter two introduces the student to Calculus of Variation and related applications in Classical Mechanics. The book is divided into two volumes: chapters 1 through 5 together form the first volume and the rest (chapters 6 to 10) form the second volume. Chapter 7 is devoted to Green's function while chapter 10 is devoted to Group Theory. The book isn't easy! For a gentler introduction to the subjects of inner product spaces and Hilbert spaces, I would highly recommend Linear Algebra and Matrix Theory by Gilbert and Gilbert. It's an excellent book on the subject and a really easy book to read. The chapters are short, the problems and examples are sufficient, and the development is complete. If you're a physics undergrad, then this is really all you'd need.
Review: Best of Both Worlds - This book is a rigorous approach to many of the math subjects relevant to physics: vector and Hilbert spaces, Special functions (Sturm-Liouville theory), Complex analysis, Group theory, and Green's functions, etc. Make no mistake, it is indeed first and foremost a math book, not a physics one. It has a high level of rigor, being very precise and thorough with definitions and using those definitions in subsequent, detailed proofs of important theorems. At the same time however, the theorems that this book proves, examples used, and guiding philosophy is very much based in what a physicist would find interesting and relevant to coursework in upper division courses highlighted in a way that is a bit more informative than what one would find in a physics textbook. Its strength lies in teaching math to a physics student interested in learning the proofs and underlying framework for the math used in a "whole, from the ground up" approach rather than the rather piecemeal approach to math in physics courses. However, one can also skip the proofs and just read the theorems and examples to get at the important information needed to calculate "stuff".

## Technical Specifications

| Specification | Value |
|---------------|-------|
| Best Sellers Rank | #249,896 in Books ( See Top 100 in Books ) #72 in Mathematical Physics (Books) #246 in Quantum Theory (Books) #1,936 in Mathematics (Books) |
| Customer Reviews | 4.6 4.6 out of 5 stars (235) |
| Dimensions  | 6.12 x 1.24 x 9.19 inches |
| Edition  | Revised ed. |
| ISBN-10  | 048667164X |
| ISBN-13  | 978-0486671642 |
| Item Weight  | 10.4 ounces |
| Language  | English |
| Print length  | 661 pages |
| Publication date  | August 20, 1992 |
| Publisher  | Dover Publications |

## Images

![Mathematics of Classical and Quantum Physics (Dover Books on Physics) - Image 1](https://m.media-amazon.com/images/I/71ipzH++HiL.jpg)

## Customer Reviews

### ⭐⭐⭐⭐⭐ A Masterpiece
*by G***T on December 29, 2019*

This book is nothing short of a mathematical symphony! One of the best books on the subject of Hilbert Spaces and Inner Product Spaces (in addition to Fourier series and transform). The subject of inner product spaces is a subtle one and the authors do a superb job in developing it piece by piece in the most elegant way I've seen (so far). Chapters 3, 4, and 5 are devoted to the development of the subjects of inner product spaces, Hilbert Spaces, and related concepts such as Linear Transformations, Eigenvalues and Eigenvectors, and Orthogonality and Completeness. For a physics student, the materials in the these three chapters is all they'd need to manage through a Quantum Mechanics course at the level of both Griffiths' Introduction to Quantum Mechanics and Shankar's Principles of Quantum Mechanics and similar books (such as my favorite book on quantum mechanics: A Modern Approach to Quantum Mechanics by John Townsend). All the polynomials such Hermite, Legendre, and Laguerre polynomials which are necessary to understand the derivations of the various eigen-functions in QM are nicely developed early on in the book. I should also mention that the first two chapters of the book dealing with mathematics of Classical Mechanics are also extremely useful. Chapter two introduces the student to Calculus of Variation and related applications in Classical Mechanics. The book is divided into two volumes: chapters 1 through 5 together form the first volume and the rest (chapters 6 to 10) form the second volume. Chapter 7 is devoted to Green's function while chapter 10 is devoted to Group Theory. The book isn't easy! For a gentler introduction to the subjects of inner product spaces and Hilbert spaces, I would highly recommend Linear Algebra and Matrix Theory by Gilbert and Gilbert. It's an excellent book on the subject and a really easy book to read. The chapters are short, the problems and examples are sufficient, and the development is complete. If you're a physics undergrad, then this is really all you'd need.

### ⭐⭐⭐⭐⭐ Best of Both Worlds
*by V***N on August 17, 2020*

This book is a rigorous approach to many of the math subjects relevant to physics: vector and Hilbert spaces, Special functions (Sturm-Liouville theory), Complex analysis, Group theory, and Green's functions, etc. Make no mistake, it is indeed first and foremost a math book, not a physics one. It has a high level of rigor, being very precise and thorough with definitions and using those definitions in subsequent, detailed proofs of important theorems. At the same time however, the theorems that this book proves, examples used, and guiding philosophy is very much based in what a physicist would find interesting and relevant to coursework in upper division courses highlighted in a way that is a bit more informative than what one would find in a physics textbook. Its strength lies in teaching math to a physics student interested in learning the proofs and underlying framework for the math used in a "whole, from the ground up" approach rather than the rather piecemeal approach to math in physics courses. However, one can also skip the proofs and just read the theorems and examples to get at the important information needed to calculate "stuff".

### ⭐⭐⭐⭐⭐ An excellent advanced text.
*by M***N on August 29, 2005*

This book gives an excellent coverage of mathematical physics from the standpoint of a vector space. It takes all of the mathematics that would normally be spread out over many courses and brings it together in one book. The treatment given here is concise and complete. It is well written and easy to follow unlike some texts. As other reviewers have said, this book is for advanced students. People with a strong mathematical background should gain a lot from this book. Undergraduates would probably find most of this book too hard. However, because this book is so good, undergraduates with an interest in mathematical physics could also gain a lot from this book. Coming from Dover this book is not only very good, it is very cheap, which makes it extremely good value. I highly recommend it.

## Frequently Bought Together

- Mathematics of Classical and Quantum Physics (Dover Books on Physics)
- Mathematics for Physicists (Dover Books on Physics)
- Theoretical Physics (Dover Books on Physics)

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*Last updated: 2026-02-27*