Mathematics of Classical and Quantum Physics

Paperback (Print)
Buy Used
Buy Used from
(Save 41%)
Item is in good condition but packaging may have signs of shelf wear/aging or torn packaging.
Condition: Used – Good details
Used and New from Other Sellers
Used and New from Other Sellers
from $6.81
Usually ships in 1-2 business days
(Save 72%)
Other sellers (Paperback)
  • All (32) from $6.81   
  • New (16) from $13.78   
  • Used (16) from $6.81   


This textbook is designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Organized around the central concept of a vector space, the book includes numerous physical applications in the body of the text as well as many problems of a physical nature. It is also one of the purposes of this book to introduce the physicist to the language and style of mathematics as well as the content of those particular subjects with contemporary relevance in physics.
Chapters 1 and 2 are devoted to the mathematics of classical physics. Chapters 3, 4 and 5 — the backbone of the book — cover the theory of vector spaces. Chapter 6 covers analytic function theory. In chapters 7, 8, and 9 the authors take up several important techniques of theoretical physics — the Green's function method of solving differential and partial differential equations, and the theory of integral equations. Chapter 10 introduces the theory of groups. The authors have included a large selection of problems at the end of each chapter, some illustrating or extending mathematical points, others stressing physical application of techniques developed in the text.
Essentially self-contained, the book assumes only the standard undergraduate preparation in physics and mathematics, i.e. intermediate mechanics, electricity and magnetism, introductory quantum mechanics, advanced calculus and differential equations. The text may be easily adapted for a one-semester course at the graduate or advanced undergraduate level.

Read More Show Less

Editorial Reviews

A republication in one volume of the two-volume Addison-Wesley edition of 1969-70, this textbook is designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Annotation c. Book News, Inc., Portland, OR (
Read More Show Less

Product Details

  • ISBN-13: 9780486671642
  • Publisher: Dover Publications
  • Publication date: 8/20/1992
  • Series: Dover Books on Physics Series
  • Edition description: Reprint
  • Pages: 665
  • Sales rank: 239,771
  • Product dimensions: 6.12 (w) x 9.19 (h) x 1.24 (d)

Table of Contents

1 Vectors in Classical Physics
    1.1 Geometric and Algebraic Definitions of a Vector
    1.2 The Resolution of a Vector into Components
    1.3 The Scalar Product
    1.4 Rotation of the Coordinate System: Orthogonal Transformations
    1.5 The Vector Product
    1.6 A Vector Treatment of Classical Orbit Theory
    1.7 Differential Operations on Scalar and Vector Fields
    *1.8 Cartesian-Tensors
2 Calculus of Variations
    2.1 Some Famous Problems
    2.2 The Euler-Lagrange Equation
    2.3 Some Famous Solutions
    2.4 Isoperimetric Problems - Constraints
    2.5 Application to Classical Mechanics
    2.6 Extremization of Multiple Integrals
    2.7 Invariance Principles and Noether's Theorem
3 Vectors and Matrics
    3.1 "Groups, Fields, and Vector Spaces"
    3.2 Linear Independence
    3.3 Bases and Dimensionality
    3.4 Ismorphisms
    3.5 Linear Transformations
    3.6 The Inverse of a Linear Transformation
    3.7 Matrices
    3.8 Determinants
    3.9 Similarity Transformations
    3.10 Eigenvalues and Eigenvectors
    *3.11 The Kronecker Product
4. Vector Spaces in Physics
    4.1 The Inner Product
    4.2 Orthogonality and Completeness
    4.3 Complete Ortonormal Sets
    4.4 Self-Adjoint (Hermitian and Symmetric) Transformations
    4.5 Isometries-Unitary and Orthogonal Transformations
    4.6 The Eigenvalues and Eigenvectors of Self-Adjoint and Isometric Transformations
    4.7 Diagonalization
    4.8 On The Solvability of Linear Equations
    4.9 Minimum Principles
    4.10 Normal Modes
    4.11 Peturbation Theory-Nondegenerate Case
    4.12 Peturbation Theory-Degenerate Case
5. Hilbert Space-Complete Orthonormal Sets of Functions
    5.1 Function Space and Hilbert Space
    5.2 Complete Orthonormal Sets of Functions
    5.3 The Dirac d-Function
    5.4 Weirstrass's Theorem: Approximation by Polynomials
    5.5 Legendre Polynomials
    5.6 Fourier Series
    5.7 Fourier Integrals
    5.8 Sphereical Harmonics and Associated Legendre Functions
    5.9 Hermite Polynomials
    5.10 Sturm-Liouville Systems-Orthogaonal Polynomials
    5.11 A Mathematical Formulation of Quantum Mechanics
6 Elements and Applications of the Theory of Analytic Functions
    6.1 Analytic Functions-The Cauchy-Riemann Conditions
    6.2 Some Basic Analytic Functions
    6.3 Complex Integration-The Cauchy-Goursat Theorem
    6.4 Consequences of Cauchy's Theorem
    6.5 Hilbert Transforms and the Cauchy Principal Value
    6.6 An Introduction to Dispersion Relations
    6.7 The Expansion of an Analytic Function in a Power Series
    6.8 Residue Theory-Evaluation of Real Definite Integrals and Summation of Series
    6.9 Applications to Special Functions and Integral Representations
7 Green's Function
    7.1 A New Way to Solve Differential Equations
    7.2 Green's Functions and Delta Functions
    7.3 Green's Functions in One Dimension
    7.4 Green's Functions in Three Dimensions
    7.5 Radial Green's Functions
    7.6 An Application to the Theory of Diffraction
    7.7 Time-dependent Green's Functions: First Order
    7.8 The Wave Equation
8 Introduction to Integral Equations
    8.1 Iterative Techniques-Linear Integral Operators
    8.2 Norms of Operators
    8.3 Iterative Techniques in a Banach Space
    8.4 Iterative Techniques for Nonlinear Equations
    8.5 Separable Kernels
    8.6 General Kernels of Finite Rank
    8.7 Completely Continuous Operators
9 Integral Equations in Hilbert Space
    9.1 Completely Continuous Hermitian Operators
    9.2 Linear Equations and Peturbation Theory
    9.3 Finite-Rank Techniques for Eigenvalue Problems
    9.4 the Fredholm Alternative for Completely Continuous Operators
    9.5 The Numerical Solutions of Linear Equations
    9.6 Unitary Transformations
10 Introduction to Group Theory
    10.1 An Inductive Approach
    10.2 The Symmetric Groups
    10.3 "Cosets, Classes, and Invariant Subgroups"
    10.4 Symmetry and Group Representations
    10.5 Irreducible Representations
    10.6 "Unitary Representations, Schur's Lemmas, and Orthogonality Relations"
    10.7 The Determination of Group Representations
    10.8 Group Theory in Physical Problems
General Bibliography
Index to Volume One
Index to Volume Two
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)