Angular Momentum
1996 Lectures in Streaming Audio below
October 22, 1996
Lecture 10-22-96: Angular Momentum in Quantum Mechanics
Conservation of Angular Momentum
Connection between Angular Momentum and Rotations
Rotational Invariance of the Hamiltonian
Taylor Expansion about the Rotated Coordinate and the Rotation Operator
Total Angular Momentum in Spherical Polar Coordinates
Matrix Elements in Hilbert Space
Raising and Lowering Operators
Angular Momentum Eigenvalue Relationships
Angular Momentum Quantum Numbers
Matrix Elements of Angular Momentum Components
Electron in an Inhomogeneous Field
Spin Angular Momentum in a Magnetic Field
October 24, 1996
Lecture 10-24-96: Angular Momentum - Normalization and Matrix Elements.
Application of Spin in a Magnetic Field
Normalization and Matrix Elements K
Atom in an Inhomogeneous Field: Stern Gerlach Effect
Force on Atom in an Inhomogeneous Field
Energy of Electron Magnetic Moment in a Magnetic Field
Arbitrary Orientation of the External Magnetic Field
October 28, 1996
Lecture 10-28-96:
Angular Momentum - Rigid Body Rotation. Euler Angles
Rotation of a Rigid Body Continued
Orientation of a Rigid Body in Space
Quantum Numbers for a Symmetric Top Rotor
Diagonalization of Inertial Matrix
Diatomic Rotor & Spherical Top
A Simple Perturbed Diatomic Rotor
Matrix Elements in the Angular Momentum Representation
Eigenfunctions: First Row of Similarity Transformation
Eigenfunctions: Normalized First Row
Eigenfunctions: Second Row of Matrix
Eigenfunctions: Normalized Transformation
Eigenfunctions: Third Eigenvalue
Complete Similarity Transformation
Coupling of Two Angular Momenta - Coupled
Scheme
Uncoupled Representation Continued F
October 30, 1996
Lecture 10-30-96:
Coupling of Two Angular Momenta - Coupled Representation and the Uncoupled Representation
Addition of Two Angular Momenta Continued
Coupled Angular Momenta Precessing in a Field
Case 1: Hamiltonian and Matrix Elements
Case 2: Precessing Angular Momenta
Case 2: Uncoupled Representation
Relation between Coupling Schemes
Vector or Clebsch-Gordon Coefficients
Calculaton of Clebsch-Gordon Coefficients
November 5, 1996
Lecture 11-5-96:
Angular Momentum - Coupled and Uncoupled Representations - Wigner 3j Symbols
Jz Operating on the Totally Stretched Ket |J,j1 + j2;j1,j2)
J^2 Operating on the Totally Stretched Ket |J,j1 + j2;j1,j2)
The Totally Stretched Ket less 1 |J,j1 + j2 -1;j1,j2)
Raising Operator on |J,j1 + j2 -1;j1,j2)
Clebsch-Gordon Coefficient from two Simultaneous Equations
Definition of Wigner 3j Symbol
Properties of the Wigner 3j Symbol
More Properties of the Wigner 3j Symbol
Formulas for some Wigner 3j Symbol
Introduction to the Wigner-Eckart Theorem
Spherical Tensors and the Wigner Eckart Theorem
Rotations of a Spherical Tensor
Illustration of Wigner-Eckart Theorem applied to an Electronic Wave Function
Mapping of a Tensor from one Coordinate System to another
November 7, 1996
Lecture 11-7-96:
Wigner Eckart Theorem
Wigner-Eckart Theorem using Spherical Harmonics cont.
Spherical Tensor Notation for Cartesian Vectors in Spherical Polar Coordinates
Comparison with Spherical Harmonics
Rotation of a Spherical Harmonic
Rotation of a Spherical Tensor
General Commutation Relations for Spherical Tensors
A Commutator leading to the Wigner-Eckart Theorem
Double Bar Matrix Elements for the Spherical Harmonics
Double Bar Matrix Elements continued
Spherical Tensors and Applications(ram file)
Spherical Tensors and Applications (2.8MB
download!)
Spherical Tensors and Applications A
Symmetric Top in an Electric Field
Commutation Relations between Spherical Tensors and Angular Momentum
Operators
Introduction to the Zeeman Effect on an Atom with
Spin-Orbit Coupling
Zeeman Effect - Coupled Representation
Coupled Representation Continued
Wigner-Eckart Theorem Applied to the Coupled Representation for the Zeeman Effect
Uncoupled Representation for the Zeeman Effect
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