Quantum Theory of Angular Momentum

Book Details

Title	Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols
Authors	D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii
Publisher	World Scientific
Year	1988
Edition	Revised reprint and English translation of the original Russian work
Language	English
Pages	528
ISBN	9789971509965
Main Category	Physics
Subject	Quantum angular momentum, mathematical physics, nuclear physics, atomic and molecular physics
Series	Unknown
Size	131 MB
Extension	PDF

Quantum Theory of Angular Momentum Summary

Quantum Theory of Angular Momentum is a comprehensive advanced handbook written by D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii. Published in English by World Scientific in 1988, it presents the mathematical framework required to understand and calculate angular momentum quantities throughout quantum physics. Rather than functioning only as an introductory textbook, the book is organized as a detailed reference that readers can consult when solving specialized theoretical or computational problems. Its coverage connects abstract mathematical methods with the notation, coefficients, functions, and identities used in practical physical calculations. The work remains especially valuable because angular momentum theory is fundamental to the description of rotations, spin, atomic states, molecular spectra, nuclear transitions, and particle interactions.

The book begins with the necessary elements of vector and tensor analysis before developing quantum angular momentum operators and their algebraic properties. It then examines irreducible tensors, tensor products, spherical tensor operators, rotation matrices, Wigner D-functions, and several classes of spherical harmonics. Considerable attention is devoted to the coupling of two or more angular momenta through Clebsch-Gordan coefficients, 3j symbols, 6j symbols, 9j symbols, and generalized 3nj symbols. The authors study symmetry relations, permutation properties, orthogonality conditions, recurrence formulas, transformation laws, and graphical techniques used to manipulate these quantities. By bringing these subjects together, the book provides a unified mathematical language for calculations that would otherwise require consultation of many separate references.

A major practical strength of the volume is its extensive collection of formulas, identities, conversion rules, and numerical information. Many expressions are presented in alternative coordinate systems and notation conventions, helping readers compare results obtained from different textbooks, research papers, or schools of theoretical physics. The discussions support calculations involving matrix elements, rotations of quantum states, multipole expansions, polarization phenomena, transition amplitudes, spin functions, and coupled-particle systems. Researchers can use the book to verify phase conventions, simplify tensor expressions, evaluate coupling coefficients, and identify symmetry properties before beginning lengthy numerical computations. This reference-oriented design makes it useful both when deriving a result from first principles and when checking the consistency of an existing calculation.

The book is best suited to advanced undergraduate students, master's students, doctoral researchers, lecturers, and professional scientists who already understand the foundations of quantum mechanics and linear algebra. Familiarity with operators, eigenstates, complex vector spaces, matrix mechanics, and elementary group theory will make the material considerably easier to follow. Its applications extend across nuclear and particle physics, atomic and molecular spectroscopy, quantum chemistry, plasma physics, collision and reaction theory, astrophysics, and mathematical physics. Readers seeking a light conceptual introduction may find the density of formulas demanding, but those performing serious calculations will benefit from the book's breadth and systematic organization. As a result, Quantum Theory of Angular Momentum serves less as a book to read once from beginning to end and more as a long-term technical companion for research and advanced study.

Key Features

• The book develops the vector and tensor foundations required for advanced angular momentum calculations.
• It explains the algebra, eigenvalues, eigenvectors, and commutation relations of quantum angular momentum operators.
• It provides a systematic treatment of irreducible tensors and spherical tensor operators.
• It examines Wigner D-functions and their role in representing finite rotations of quantum states.
• It covers scalar, vector, spinor, and tensor spherical harmonics used in physical expansions.
• It presents detailed properties of Clebsch-Gordan coefficients and equivalent 3j-symbol notation.
• It studies Racah coefficients, 6j symbols, 9j symbols, and generalized 3nj coupling symbols.
• It includes symmetry, orthogonality, permutation, recurrence, and summation relations for coupling coefficients.
• It compares notation and phase conventions used by different authors in the angular momentum literature.
• It gives formulas in multiple coordinate systems to support transformations between physical reference frames.
• It supplies analytical expressions and numerical tables useful for checking theoretical and computational results.
• It supports applications in nuclear physics, particle physics, spectroscopy, collision theory, plasma physics, and quantum chemistry.
• It is structured as a searchable reference handbook suitable for repeated consultation during research.

About the Authors

Dmitry Alexandrovich Varshalovich was a Soviet and Russian theoretical physicist and astrophysicist born in Leningrad in 1934. He graduated from the Physics Faculty of Leningrad State University in 1957 with a specialization in nuclear spectroscopy and began his scientific career at the institution now known as the Ioffe Institute. His research covered nuclear spectroscopy, quantum and radiation theory, interstellar molecular physics, quasar spectroscopy, cosmology, and possible variations of fundamental physical constants. He became a Doctor of Physical and Mathematical Sciences, a professor, a chief research scientist at the Ioffe Institute, and a full member of the Russian Academy of Sciences. Varshalovich authored or co-authored more than two hundred scientific publications, taught generations of physics students, and received distinctions including the Fock Prize, the Belopolsky Prize, and the Russian Federation State Prize in Science and Technology.

A. N. Moskalev was a Soviet and Russian theoretical physicist associated with the Petersburg Nuclear Physics Institute and its theoretical physics activities. His work included angular momentum theory, atomic physics, and problems involving weak interactions, and he held senior scientific and institutional responsibilities during his career. Moskalev and Varshalovich received the V. A. Fock Prize for their work on the Russian monograph devoted to the quantum theory of angular momentum. V. K. Khersonskii was a physicist and long-term collaborator of Varshalovich whose research contributions included angular momentum methods, interstellar molecular spectroscopy, and theoretical studies of matter in astrophysical environments. Detailed verified information about Khersonskii's education, formal academic appointments, and awards is unavailable.

Related Books

• Angular Momentum in Quantum Mechanics — A. R. Edmonds
• Elementary Theory of Angular Momentum — Morris E. Rose
• Angular Momentum — D. M. Brink and G. R. Satchler
• Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics — Richard N. Zare
• Angular Momentum in Quantum Physics: Theory and Application — L. C. Biedenharn and James D. Louck
• The Racah-Wigner Algebra in Quantum Theory — L. C. Biedenharn and James D. Louck
• Angular Momentum Techniques in Quantum Mechanics — V. Devanathan

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Frequently Asked Questions

Q: Which edition of Quantum Theory of Angular Momentum is presented here?

A: This page concerns the English edition published by World Scientific in 1988. Bibliographic catalogues describe it as a revised reprint and as a translation of an earlier Russian work on the same subject. The English edition made the authors' extensive collection of formulas and angular momentum tables accessible to a broader international research community.

Q: Does the book only provide tables, or does it also explain the underlying theory?

A: The book contains much more than numerical tables. It develops the mathematical theory of vectors, tensors, rotations, angular momentum operators, spherical harmonics, and coupling coefficients before presenting specialized formulas and tabulated results. Readers can therefore use it both to study derivations and to retrieve specific identities during calculations.

Q: What mathematical background is needed to study this book effectively?

A: Readers should already understand linear algebra, complex numbers, matrices, eigenvalue problems, differential equations, and the basic postulates of quantum mechanics. Some familiarity with operator methods, group representations, and tensor notation is also helpful. The book is generally more appropriate for advanced students and researchers than for complete beginners.

Q: Which angular momentum coefficients and symbols are covered?

A: The volume treats Clebsch-Gordan coefficients, 3j symbols, Racah coefficients, 6j symbols, 9j symbols, and more general 3nj symbols. It examines their definitions, symmetry properties, phase conventions, orthogonality relations, recurrence formulas, and transformation rules. These tools are central to coupling and recoupling several quantum angular momenta.

Q: Is the book useful for atomic and molecular spectroscopy?

A: Yes, angular momentum coupling is essential for describing atomic and molecular energy levels, selection rules, polarization, rotational states, and transition amplitudes. The book's treatment of spherical tensors, Wigner functions, spin functions, and matrix elements is directly relevant to spectroscopy. It can also help researchers translate between different notation conventions used in spectroscopy literature.

Q: Can the formulas be used in numerical or computer-based calculations?

A: Yes, many of the identities, symmetry rules, recurrence relations, and tabulated coefficients can support computational implementations. The book predates modern symbolic and numerical software, so it does not provide code in contemporary programming languages. Nevertheless, its formulas can be implemented in systems such as Mathematica, MATLAB, Python, Julia, or specialized quantum-physics software.

Q: Why do some catalogues report 514 pages while the digital edition contains 528 pages?

A: Different catalogues may count only the numbered main text while digital platforms may include preliminary pages, title pages, contents, or other front matter in the total. The print bibliographic record is frequently listed as x plus 514 pages, whereas some electronic editions report 528 pages. The PDF described on this page follows the 528-page digital count.