Next:
Preface
Q
UANTUM
P
HYSICS 130
B
August 1, 1998
Preface
Operators Matrices and Spin
The Matrix Representation of Operators and Wavefunctions
The Angular Momentum Matrices
Eigenvalue Problems with Matrices
Rotation operators for
An
System in a Magnetic Field
Spin
A Two State System: The Ammonia Maser
The Two State Neutral Kaon System
Examples
Harmonic Oscillator Hamiltonian Matrix
Harmonic Oscillator Raising Operator
Harmonic Oscillator Lowering Operator
Eigenvectors of
The Stern-Gerlach Experiment
A Rotated Stern-Gerlach Apparatus
Energy Eigenstates of an
System in a B-field
Time Development of an
System in a B-field: Version I
Expectation of
in General Spin
State
Eigenvectors of
for Spin
Eigenvectors of
for Spin
Time Development of a Spin
State in a B field
Nuclear Magnetic Resonance (NMR and MRI)
Derivations and Computations
The
Angular Momentum Operators
Compute
Using Matrices.
Derive the Expression for Rotation Operator
Compute the
Rotation Operator
Compute the
Rotation Operator
Derive Spin
Operators
Derive Spin
Rotation Matrices
NMR Transition Rate in a Oscillating B Field
Homework Problems
Sample Test Problems
Electrons in an Electromagnetic Field
The Equations of Electricity and Magnetism in CGS Units
The Quantum Hamiltonian Including a B-field
A Plasma in a Magnetic Field
Gauge Symmetry in Quantum Mechanics
Examples
Derivations and Computations
The Lorentz Force from the Classical Hamiltonian
The Hamiltonian in terms of B
The Size of the B field Terms in Atoms
The Naive Zeeman Splitting
Energy States of Electrons in a Plasma I
Energy States of Electrons in a Plasma II
A Hamiltonian Invariant Under Wavefunction Phase (or Gauge) Transformations
Magnetic Flux Quantization from Gauge Symmetry
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
General Addition of Angular Momentum: The Clebsch-Gordan Series
Interchange Symmetry for States with Identical Particles
Examples
Counting states for
Plus spin
Counting states for Arbitrary
Plus spin
Adding
to
The parity of the pion from
.
Derivations and Computations
Commutators of Total Spin Operators
Using the Lowering Operator to Find Total Spin States
Applying the
Operator to
and
.
Adding any
plus spin
.
Counting the States for
.
Homework Problems
Sample Test Problems
Time Independent Perturbation Theory
The Perturbation Series
Degenerate State Perturbation Theory
Examples
H.O. with anharmonic perturbation (
).
Hydrogen Atom in a E-field, the Stark Effect.
The Stark Effect for n=2 Hydrogen.
Derivations and Computations
Derivation of 1st and 2nd Order Perturbation Equations
Derivation of 1st Order Degenerate Perturbation Equations
Homework Problems
Sample Test Problems
Fine Structure in Hydrogen
Hydrogen Fine Structure
Hydrogen Atom in a Weak Magnetic Field
Examples
Hydrogen Fine Structure for
Zeeman Effect for
Zeeman Effect for
Derivations and Computations
The Relativistic Correction
The Spin-Orbit Correction
Perturbation Calculation for Relativistic Energy Shift
Perturbation Calculation for H2 Energy Shift
The Darwin Term
The Anomalous Zeeman Effect
Homework Problems
Sample Test Problems
Hyperfine Structure
Hyperfine Splitting
Hyperfine Splitting in a B Field
Examples
Splitting of the Hydrogen Ground State
Hyperfine Splitting in a Weak B Field
Hydrogen in a Strong B Field
Intermediate Field
Positronium
Hyperfine and Zeeman for H, muonium, positronium
Derivations and Computations
Hyperfine Correction in Hydrogen
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
1D Harmonic Oscillator
1-D H.O. with exponential wavefunction
Derivations and Computations
Calculation of the ground state energy shift
Homework Problems
Sample Test Problems
Atomic Physics
Atomic Shell Model
The Hartree Equations
Hund's Rules
The Nuclear Shell Model
Examples
Boron Ground State
Carbon Ground State
Nitrogen Ground State
Oxygen Ground State
Homework Problems
Sample Test Problems
Molecular Physics
The H
Ion
The H
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, the Second Quantization, and Radiation in Atoms
Examples
Derivations and Computations
Homework Problems
Sample Test Problems
About this document ...
James Branson
2001-09-17
System in a Magnetic Field
System in a B-field
System in a B-field: Version I
in General Spin
State
for Spin
for Spin
State in a B field
to Integer Orbital Angular Momentum
![\bgroup\color{black}$[L_x,L_y]$\egroup](img251.gif){kind=small}
Using Matrices.
Plus spin
Plus spin
to
.
Operator to
and
.
.
).
Ion
Molecule