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Preface
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Quantum Physics 130
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Quantum Physics 130
Contents
Course Summary
Problems with Classical Physics
Thought Experiments on Diffraction
Probability Amplitudes
Wave Packets and Uncertainty
Operators
Expectation Values
Commutators
The Schrödinger Equation
Eigenfunctions, Eigenvalues and Vector Spaces
A Particle in a Box
Piecewise Constant Potentials in One Dimension
The Harmonic Oscillator in One Dimension
Delta Function Potentials in One Dimension
Harmonic Oscillator Solution with Operators
More Fun with Operators
Two Particles in 3 Dimensions
Identical Particles
Some 3D Problems Separable in Cartesian Coordinates
Angular Momentum
Solutions to the Radial Equation for Constant Potentials
Hydrogen
Solution of the 3D HO Problem in Spherical Coordinates
Matrix Representation of Operators and States
A Study of
Operators and Eigenfunctions
Spin 1/2 and other 2 State Systems
Quantum Mechanics in an Electromagnetic Field
Local Phase Symmetry in Quantum Mechanics and the Gauge Symmetry
Addition of Angular Momentum
Time Independent Perturbation Theory
The Fine Structure of Hydrogen
Hyperfine Structure
The Helium Atom
Atomic Physics
Molecules
Time Dependent Perturbation Theory
Radiation in Atoms
Classical Field Theory
The Classical Electromagnetic Field
Quantization of the EM Field
Scattering of Photons
Electron Self Energy
The Dirac Equation
The Dirac Equation
The Problems with Classical Physics
Black Body Radiation *
The Photoelectric Effect
The Rutherford Atom *
Atomic Spectra *
Derivations and Computations
Examples
Sample Test Problems
Diffraction
Diffraction from Two Slits
Single Slit Diffraction
Diffraction from Crystals
The DeBroglie Wavelength
Wave Particle Duality (Thought Experiments)
Examples
Sample Test Problems
The Solution: Probability Amplitudes
Derivations and Computations
Sample Test Problems
Wave Packets
Building a Localized Single-Particle Wave Packet
Two Examples of Localized Wave Packets
The Heisenberg Uncertainty Principle
Position Space and Momentum Space
Time Development of a Gaussian Wave Packet *
Derivations and Computations
Examples
Sample Test Problems
Operators
Operators in Position Space
Operators in Momentum Space
Expectation Values
Dirac Bra-ket Notation
Commutators
Derivations and Computations
Examples
Sample Test Problems
The Schrödinger Equation
Deriving the Equation from Operators
The Flux of Probability *
The Schrödinger Wave Equation
The Time Independent Schrödinger Equation
Derivations and Computations
Examples
Sample Test Problems
Eigenfunctions, Eigenvalues and Vector Spaces
Eigenvalue Equations
Hermitian Conjugate of an Operator
Hermitian Operators
Eigenfunctions and Vector Space
The Particle in a 1D Box
Momentum Eigenfunctions
Derivations and Computations
Examples
Sample Test Problems
One Dimensional Potentials
Piecewise Constant Potentials in 1D
The 1D Harmonic Oscillator
The Delta Function Potential *
The Delta Function Model of a Molecule *
The Delta Function Model of a Crystal *
The Quantum Rotor
Derivations and Computations
Examples
Sample Test Problems
Harmonic Oscillator Solution using Operators
Introducing
and
Commutators of
,
and
Use Commutators to Derive HO Energies
Expectation Values of
and
The Wavefunction for the HO Ground State
Examples
Sample Test Problems
More Fun with Operators
Operators in a Vector Space
A Complete Set of Mutually Commuting Operators
Uncertainty Principle for Non-Commuting Operators
Time Derivative of Expectation Values *
The Time Development Operator *
The Heisenberg Picture *
Examples
Sample Test Problems
Extending QM to Two Particles and Three Dimensions
Quantum Mechanics for Two Particles
Quantum Mechanics in Three Dimensions
Two Particles in Three Dimensions
Identical Particles
Sample Test Problems
3D Problems Separable in Cartesian Coordinates
Particle in a 3D Box
The 3D Harmonic Oscillator
Sample Test Problems
Angular Momentum
Rotational Symmetry
Angular Momentum Algebra: Raising and Lowering Operators
The Angular Momentum Eigenfunctions
Derivations and Computations
Examples
Sample Test Problems
The Radial Equation and Constant Potentials *
The Radial Equation *
Behavior at the Origin *
Spherical Bessel Functions *
Particle in a Sphere *
Bound States in a Spherical Potential Well *
Partial Wave Analysis of Scattering *
Scattering from a Spherical Well *
The Radial Equation for
*
Sample Test Problems
Hydrogen
The Radial Wavefunction Solutions
The Hydrogen Spectrum
Derivations and Calculations
Examples
Sample Test Problems
3D Symmetric HO in Spherical Coordinates *
Operators Matrices and Spin
The Matrix Representation of Operators and Wavefunctions
The Angular Momentum Matrices*
Eigenvalue Problems with Matrices
An
System in a Magnetic Field
*
Splitting the Eigenstates with Stern-Gerlach
Rotation operators for
*
A Rotated Stern-Gerlach Apparatus*
Spin
Other Two State Systems*
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
Homework Problems 130A
HOMEWORK 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Homework 8
Homework 9
Electrons in an Electromagnetic Field
Review of the Classical Equations of Electricity and Magnetism in CGS Units
The Quantum Hamiltonian Including a B-field
Gauge Symmetry in Quantum Mechanics
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
Addition of Angular Momentum
Adding the Spins of Two Electrons
Total Angular Momentum and The Spin Orbit Interaction
Adding Spin
to Integer Orbital Angular Momentum
Spectroscopic Notation
General Addition of Angular Momentum: The Clebsch-Gordan Series
Interchange Symmetry for States with Identical Particles
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
Time Independent Perturbation Theory
The Perturbation Series
Degenerate State Perturbation Theory
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
Fine Structure in Hydrogen
Hydrogen Fine Structure
Hydrogen Atom in a Weak Magnetic Field
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
Hyperfine Structure
Hyperfine Splitting
Hyperfine Splitting in a B Field
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
The Helium Atom
General Features of Helium States
The Helium Ground State
The First Excited State(s)
The Variational Principle (Rayleigh-Ritz Approximation)
Variational Helium Ground State Energy
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
Atomic Physics
Atomic Shell Model
The Hartree Equations
Hund's Rules
The Periodic Table
The Nuclear Shell Model
Examples
Homework Problems
Sample Test Problems
Molecular Physics
The
Ion
The
Molecule
Importance of Unpaired Valence Electrons
Molecular Orbitals
Vibrational States
Rotational States
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
Time Dependent Perturbation Theory
General Time Dependent Perturbations
Sinusoidal Perturbations
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
Radiation in Atoms
The Photon Field in the Quantum Hamiltonian
Decay Rates for the Emission of Photons
Phase Space: The Density of Final States
Total Decay Rate Using Phase Space
Electric Dipole Approximation and Selection Rules
Explicit 2p to 1s Decay Rate
General Unpolarized Initial State
Angular Distributions
Vector Operators and the Wigner Eckart Theorem
Exponential Decay
Lifetime and Line Width
Phenomena of Radiation Theory
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
Scattering
Scattering from a Screened Coulomb Potential
Scattering from a Hard Sphere
Homework Problems
Sample Test Problems
Classical Scalar Fields
Simple Mechanical Systems and Fields
Classical Scalar Field in Four Dimensions
Classical Maxwell Fields
Rationalized Heaviside-Lorentz Units
The Electromagnetic Field Tensor
The Lagrangian for Electromagnetic Fields
Gauge Invariance can Simplify Equations
Quantum Theory of Radiation
Transverse and Longitudinal Fields
Fourier Decomposition of Radiation Oscillators
The Hamiltonian for the Radiation Field
Canonical Coordinates and Momenta
Quantization of the Oscillators
Photon States
Fermion Operators
Quantized Radiation Field
The Time Development of Field Operators
Uncertainty Relations and RMS Field Fluctuations
Emission and Absorption of Photons by Atoms
Review of Radiation of Photons
Black Body Radiation Spectrum
Scattering of Photons
Resonant Scattering
Elastic Scattering
Rayleigh Scattering
Thomson Scattering
Raman Effect
Electron Self Energy Corrections
The Lamb Shift
Dirac Equation
Dirac's Motivation
The Schrödinger-Pauli Hamiltonian
The Dirac Equation
The Conserved Probability Current
The Non-relativistic Limit of the Dirac Equation
Solution of Dirac Equation for a Free Particle
``Negative Energy'' Solutions: Hole Theory
Equivalence of a Two Component Theory
Relativistic Covariance
Parity
Bilinear Covariants
Constants of the Motion for a Free Particle
The Relativistic Interaction Hamiltonian
Phenomena of Dirac States
Solution of the Dirac Equation for Hydrogen
Thomson Scattering
Hole Theory and Charge Conjugation
Charge Conjugate Waves
Quantization of the Dirac Field
The Quantized Dirac Field with Positron Spinors
Vacuum Polarization
The QED LaGrangian and Gauge Invariance
Interaction with a Scalar Field
Formulas
Jim Branson 2013-04-22