UID:
almafu_9959240255502883
Format:
1 online resource (xxxii, 716 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88608-8
,
1-107-10231-6
,
1-107-09979-X
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1-107-09371-6
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1-107-08749-X
,
0-511-75988-6
Series Statement:
Encyclopedia of mathematics and its applications ; v. 8
Content:
This 1985 text develops the theory of angular momentum from the viewpoint of a fundamental symmetry in nature and shows how this concept relates to applied areas of research in modern quantum physics.
Note:
Imprint and ISBN from label on t.p. verso. Imprint on t.p.: Reading, Mass. : Addison-Wesley, Advanced Book Program, 1981.
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Publication taken over by Cambridge University Press in 1984 with a new copyright date.
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Cover; Half-title; Title; Copyright; Dedication; Contents; Contents of Volume 9; Editor's Statement; Section Editor's Foreword; Preface; Acknowledgntents; PART I; Chapter 1 Introduction; Notes; References; Chapter 2 The Kinematics of Rotations; 1. Introduction; 2. Properties of Rotations; 3. Dirac's Construction; 4. Cartan's Definition of a Spinor; 5. Relation between SU(2) and SO(3) Rotations; 6. Parametrizations of the Group of Rotations; 7. Notes; References; Chapter 3 Standard Treatment of Angular Momentum in Quantum Mechanics; 1. Overview; 2. Definition of the Angular Momentum Operators
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3. The Angular Momentum Multiplets4. Matrices of the Angular Momentum; 5. The Rotation Matrices (General Properties); 6. The Rotation Matrices (Explicit Forms); 7. Wave Functions for Angular Momentum Systems; 8. Differential Equations for the Rotation Matrices; 9. Orthogonality of the Rotation Matrices; 10. Spherical Harmonics; 11. The Addition of Angular Momentum; 12. The Wigner Coefficients 1; 13. Relations between Rotation Matrices and Wigner Coefficients; 14. Concept of a Tensor Operator; 15. The Wigner-Eckart Theorem; 16. The Coupling of Tensor Operators
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17. Applications of the Wigner-Eckart Theorem18. Racah Coefficients; 19. 9-j Coefficients; 20. Rotationally Invariant Products; 21. Operators Associated with Wigner, Racah, and 9-j Coefficients; 22. Notes; 23. Appendices; References; Chapter 4 The Theory of Turns Adapted from Hamilton; 1. An Alternative Approach to Rotations; 2. Properties of Turns (Geometric View); 3. Properties of Turns (Algebraic View); 4. The Space of Turns as a Carrier Space; 5. Notes; References; Chapter 5 The Boson Calculus Applied to the Theory of Turns; 1. Introduction; 2. Excursus on the Boson Calculus
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3. The Jordan Mapping4. An Application of the Jordan Map; 5. Generalization of the Jordan Map; 6. Application of the Generalized Jordan Map; 7. Application of the Generalized Jordan Map to Determine the Wigner Coefficients; 8. Wigner Coefficients as ""Discretized"" Rotation Matrices; 9. Appendices; References; Chapter 6 Orbital Angular Momentum and Angular Functions on the Sphere; I. Rotational Symmetry of a Simple Physical System; 2. Scalar Product of State Vectors; 3. Unitarity of the Orbital Rotation Operator; 4. A (Dense) Subspace of H (S)
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5. Only Integral Values of I can occur in the Quantization of Spatial (Orbital) Angular Momentum6. Transformations of the Solid Harmonics under Orbital Rotation; 7. The Elements of the Rotation Matrix D1(R) are Homogeneous Polynomials; 8. The Energy Eigenvalue Equation; 9. Tensor Spherical Harmonics; 10. Spinor Spherical Harmonics; 11. Vector Spherical Harmonics; 12. Algebraic Aspects of Vector Spherical Harmonics; 13. Summary of Properties of Vector Solid Harmonics; 14. Decomposition Theorem for Vector Functions Defined on the Sphere
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15. Rotationally Invariant Spherical Functions of Two Vectors
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English
Additional Edition:
ISBN 0-521-10244-8
Additional Edition:
ISBN 0-521-30228-5
Language:
English
URL:
https://doi.org/10.1017/CBO9780511759888
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