Irreducible Tensor Methods
An Introduction for Chemists
Published on 17. September 2013
246 pages
978-1-4831-9181-2 (ISBN)
Description
Irreducible Tensor Methods: An Introduction for Chemists explains the theory and application of irreducible tensor operators. The book discusses a compact formalism to describe the effect that results on an arbitrary function of a given set of coordinates when that set is subjected to a rotation about its origin. The text also explains the concept of irreducible tensor operators, particularly, as regards the transformation properties of operators under coordinate transformations, and, in a special way, the group of rotations. The book examines the systematic construction of compound tensor operators from simple operators to classify the behavior of any operator under coordinate rotations. This classification is a significant component of the irreducible tensor method. The text explains the use of the 6-j and 9-j symbols to complete theoretical concepts that are applied in irreducible tensor methods dealing with problems of atomic and molecular physics. The book describes the matrix elements in multielectron systems, as well as the reduced matrix elements found in these systems. The book is suitable for nuclear physicists, molecular physicists, scientists, and academicians in the field of quantum mechanics or advanced chemistry.
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01/1976
Academic Press
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Content
PrefaceIntroductionPart I Chapter 1 The Rotation Operator 1.1 Coordinate Rotations 1.2 The Euler Angles 1.3 The Infinitesimal Rotation Operator 1.4 Transformed Functions 1.5 The Rotation Operator for One Axis 1.6 The Rotation Operator 1.7 Some Misconceptions 1.8 Rotations in Spin Space 1.9 An Example 1.10 The Inverse Rotation Operator 1.11 Rotation of Functions 1.12 Rotation of Operators 1.13 Comments on the Rotation Group 1.14 Comments on Lie Groups 1.15 Conventions Chapter 2 The Wigner Rotation Matrices 2.1 The Rotation Matrices 2.2 Questions of Phase 2.3 The Forms of D(1/2) and D(1) 2.4 Properties of the Rotation Matrices 2.5 The Transformation of Components of Tensors 2.6 Another Look at D(1/2) 2.7 Conventions Chapter 3 The Coupling of Two Angular Momenta 3.1 Introductory Examples 3.2 The Vector-Coupling Coefficients 3.3 A Comment on Phase 3.4 The Evaluation and Properties of the VC Coefficients 3.5 The 3-j Symbol 3.6 Evaluation of the 3-j Symbols 3.7 The Clebseh-Gordan Series 3.8 Two Useful Integrals 3.9 Regge Symmetries 3.10 The ^Coefficient 3.11 A Final Comment Chapter 4 Scalars, Vectors, Tensors 4.1 Vectors 4.2 Cartesian Tensors 4.3 Irreducible Spherical Tensors 4.4 Irreducible Cartesian Tensors 4.5 Irreducible Tensor Fields 4.6 Scalars Chapter 5 Irreducible Tensor Operators 5.1 Definition of Irreducible Tensor Operators 5.2 An Example 5.3 Racah's Commutation Relations 5.4 Scalar and Vector Operators 5.5 A Lie Group 5.6 The Construction of Compound Irreducible Tensor Operators 5.7 Scalar Operators 5.8 Standard Basis Vectors 5.9 Another Phase Convention 5.10 Comment on Contragredience 5.11 Adjoint Tensor Operators Chapter 6 The Wigner-Eckart Theorem 6.1 Introduction 6.2 Proof of the Wigner-Eckart Theorem 6.3 Comments on and Consequences of the Theorem 6.4 Parity 6.5 Selection Rules 6.6 Sum Rules 6.7 Comment on Point Groups Chapter 7 The 6-j Symbol 7.1 Introduction 7.2 Recoupling 7.3 Properties of the 6-j Symbol 7.4 Invariance of the 6-j Symbol 7.5 Regge Symmetries 7.6 A Warning Chapter 8 The 9-j Symbol 8.1 Definition of the 9-j Symbol 8.2 Properties of the 9-j Symbol 8.3 The Recoupling of Operators 8.4 Invariance of the 9-j Symbol Chapter 9 The Matrix Elements of Irreducible Tensor Operators 9.1 Introduction 9.2 Derivation of the Basic Formula 9.3 The Reduced Matrix Elements of ITOs 9.4 Double-Tensor Operators 9.5 Comments on the Basic EquationsPart II Chapter 10 The Coulomb Interaction 10.1 The Spherical Harmonic Addition Theorem 10.2 The Coulomb Splittings for p2 Chapter 11 Spin-Orbit Coupling 11.1 The Matrix Elements of the Spin-orbit Hamiltonian 11.2 The Spin-orbit Energies for the 3d2 Configuration Chapter 12 The Magnetic Dipole-Dipole Interaction 12.1 The Dipole-Dipole Hamiltonian 12.2 An Example Chapter 13 Spin-Spin Couplings Chapter 14 The Electronic Zeeman Interaction Chapter 15 Operator Equivalents 15.1 Operator Equivalents 15.2 Off-Diagonal Operator Equivalents Chapter 16 Real Tensorial Sets in R3-Cartesian Tensors Chapter 17 Some Multipole Expansions 17.1 Introduction 17.2 Plane Waves 17.3 Electronic Multipole Moments 17.
