Dec 27, 2011 Pondering a question on conditional probability. 

Dec 12, 2011 Verifying the Helmholtz Green's function.

Dec 11, 2011 Second form of adiabatic approximation.

Dec 10, 2011 Evaluating the squared sinc integral.

Dec 8, 2011 A short derivation of the time dependent pertubation result.

Dec 8, 2011 One more adiabatic pertubation derivation.

Dec 7, 2011 Born approximation.

Dec 5, 2011 3D Scattering cross sections (cont.)

Nov 30, 2011 3D Scattering.

Nov 28, 2011 Scattering (cont.)

Nov 23, 2011 Scattering theory.

Nov 23, 2011 On conditions for Clebsh-Gordan coefficients to be zero.

Nov 21, 2011 Spherical tensors.

Nov 16, 2011 Rotations of operators.

Nov 12, 2011 The Clebsch-Gordon convention for the basis elements of summed generalized angular momentum

Nov 11, 2011 Second order time evolution for the coefficients of an initially pure ket with an adiabatically changing Hamiltonian.

Nov 9, 2011 Two spin systems and angular momentum.

Nov 7, 2011 Degeneracy and diagonalization

Nov 6, 2011 Review of approximation results.

Nov 2, 2011 Hydrogen atom with spin, and two spin systems.

Oct 31, 2011 Rotation operator in spin space

Oct 28, 2011 WKB method and Stark shift.

Oct 27, 2011 A different derivation of the adiabatic perturbation coefficient equation

Oct 26, 2011 Representation of two state kets and Pauli spin matrices.

Oct 24, 2011 Spin and spinors (cont.)

Oct 19, 2011 WKB Method

Oct 17, 2011 Spin and Spinors

Oct 12, 2011 phy456 Problem set 4, problem 2 notes.

Oct 10, 2011 Fermi's golden rule (cont.)

Oct 9, 2011 Simple entanglement example.

Oct 5, 2011 Adiabatic perturbation theory (cont.)

Oct 3, 2011 Time dependent pertubation (cont.)

Sept 29, 2011 Helium atom ground state energy estimation notes.

Sept 26, 2011 Interaction picture.

Sept 25, 2011 Time dependent pertubation

Sept 23, 2011 Pertubation theory and degeneracy. Review of dynamics.

Sept 21, 2011 Time independent perturbation theory (continued)

Sept 19, 2011 Perturbation methods

Sept 12, 2011 My solutions to problem set 1 (ungraded).

Sept 12, 2011 Approximate methods.

Sept 12, 2011 Review: Composite systems

Sept 1, 2011 Covariant gauge transformation of Dirac equation to get the spin adjusted Klein-Gordon equation.
GA use of dot and wedge products to arrive at some of the Dirac equation results in Desai. In particular multiplication of the (gauge transformed) Dirac equation by a conjugate of sorts results in the Klein-Gordon equation, but with the spin terms required for electrons. 

Sept 1, 2011 Curious problem using the variational method to find the ground state energy of the Harmonic oscillator.

Aug 4, 2011 Gauge transformation of the Dirac equation.
non-Covariant gauge transformation notes for the Dirac equation, and the corresponding non-relativistic approximation.

June 20, 2011 On tensor product generators of the gamma matrices.

May 25, 2011 Dirac spinor notes.
Notes on Dirac spinor solutions.

April 30, 2011 A cylindrical Lienard-Wiechert potential calculation using multivector matrix products. 

 April 13, 2011 Some exam reflection.

April 10, 2011 Three dimensional divergence theorem with generally parametrized volume element. 

April 6, 2011 Radiation reaction force continued, and limits of classical electrodynamics. 

April 5, 2011 Radiation reaction force for a dipole system. 

Mar 31, 2011 Second order interaction, the Darwin Lagrangian. 

Mar 30, 2011 Some worked problems. EM reflection. Stress energy tensor for simple configurations. 

Mar 30, 2011 Non-relativistic electrostatic Lagrangian. 

Mar 29, 2011 Energy Momentum Tensor. 

Mar 25, 2011 Problem Set 6.

Mar 23, 2011 PHY450H1S. Relativistic Electrodynamics Tutorial 8 (TA: Simon Freedman). EM fields from magnetic dipole current.
EM fields from magnetic dipole current.

Mar 23, 2011 Energy Momentum Tensor.

Mar 22, 2011 More on EM fields due to dipole radiation. 

Mar 15, 2011 Lienard-Wiechert potentials. 

Mar 15, 2011 Potentials at a distance from a localized current distribution. EM fields due to dipole radiation

Mar 14, 2011 Problem Set 5.

Mar 10, 2011 PHY450H1S. Relativistic Electrodynamics Tutorial 5 (TA: Simon Freedman). Angular momentum of EM fields 

Mar 9, 2011 Green's function solution to Maxwell's equation. 

Mar 8, 2011 Playing with complex notation for relativistic applications in a plane 

Mar 8, 2011 Energy and momentum density. Starting a Green's function solution to Maxwell's equation. 

Mar 3, 2011 PHY450H1S. Relativistic Electrodynamics Tutorial 4 (TA: Simon Freedman). Waveguides: confined EM waves.
Waveguides: confined EM waves.

Mar 3, 2011 PHY450H1S Problem Set 4.
Problem Set 4.

Mar 2, 2011 Monochromatic EM fields. Poynting vector and energy density conservation. 

Mar 1, 2011 Fourier solution of Maxwell's vacuum wave equation in the Coulomb gauge. 

Feb 20, 2011 Exploring Stokes Theorem in tensor form. 

Feb 16, 2011 PHY450H1S. Relativistic Electrodynamics Lecture 14 (Taught by Simon Freedman). Wave equation in Coulomb and Lorentz gauges.

Wave equation in Coulomb and Lorentz gauges.

Feb 15, 2011 Variational principle for the field. 

Feb 15, 2011 PHY450H1S Problem Set 3. 

Feb 10, 2011 Action for the field.

Feb 9, 2011 Unpacking Lorentz force equation. Lorentz transformations of the strength tensor, Lorentz field invariants, Bianchi identity, and first half of Maxwell's.

Feb 8, 2011 Lorentz force equation energy term, and four vector formulation of the Lorentz force equation.

Feb 6, 2011 Energy term of the Lorentz force equation.

Feb 3, 2011 PHY450H1S. Relativistic Electrodynamics Tutorial 3 (TA: Simon Freedman). Relativistic motion in constant uniform electric or magnetic fields.
Relativistic motion in constant uniform electric or magnetic fields.

Feb 1, 2011 PHY450H1S Problem Set 2. 

Feb 1, 2011 Dynamics in a vector field. 

Feb 1, 2011 Relativistic dynamics. 

Jan 27, 2011 PHY450H1S. Relativistic Electrodynamics Tutorial 2 (TA: Simon Freedman). Two worked problems.
Two worked problems.

Jan 26, 2011 Action and relativistic dynamics. 

Jan 25, 2011 Four vectors and tensors. 

Jan 22, 2011 PHY450H1S Problem Set 1.
Problem Set 1.

Jan 20, 2011 Four vectors and a worked problem on energy flux density. 

Jan 18, 2011 Proper time, length contraction, time dialation, causality. 

Jan 18, 2011 Spacetime geometry, Lorentz transformations, Minkowski diagrams. 

Jan 14, 2011 Lorentz transformation of an antisymmetric tensor.

Some tensor and geometric algebra comparisons in a spacetime context.

Jan 13, 2011 Spacetime, events, worldlines, spacetime intervals, and invariance. 

Jan 12, 2011 Spacetime, events, worldlines, proper time, invariance. 

Jan 11, 2011 Speed of light and simultaneity. 

Jan 9, 2011 A problem on spherical harmonics.

Jan 4, 2011 Some worked problems from old PHY356 exams.