Topics in Spin

I developed and taught this seminar as a special “one-off” for graduate students in our program in 2014. My colleague, Roberto Vega, provided some lectures at the end (the helicity formalism) which are not captured in my lecture notes, since he prepared those separately. All materials are available below.

I am fascinated by quantum spin as a physical quantity. It behaves like an angular momentum, but nothing is actually spinning. Mind. Blown.

This seminar was a true joy for me to prepare, and the notes have been refined in the intervening years thanks to conversations especially with my colleague Randy Scalise.

Lecture and Class Materials

Lecture Notes for all lectures from 3/11 — 4/08

  • 2014/03/11 [FOSC 158, 1-3pm]: Introduction and Mathematical Tools
    [Solutions to Exercises] [Video]
  • 2014/03/13 [FOSC 158, 1-3pm]: Orbital Angular Momentum
    [Solutions to Exercises] [Video]
  • 2014/03/20 [FOSC 202, 2-4pm]: Spin and Addition of Angular Momentum
  • 2014/03/25 [FOSC 202, 2-4pm]: The General Problem of Adding Angular Momentum
  • 2014/03/27 [FOSC 202, 2-4pm]: Relativistic Quantum Mechanics and Spin
  • 2014/04/03 [FOSC 202, 2-4pm]: Rotations; Decay Angular Distributions (a first peek)
  • 2014/04/08 [FOSC 202, 2:30-4:30pm]: The Helicity Formalism (I) [Vega]
  • 2014/04/10 [FOSC 202, 2-3:30pm]: The Helicity Formalism (II) [Vega]

Assignments and Assessments

Topic Sequence

  • Review of the Experimental Evidence for Spin
    • A brief refresher on classical orbital angular momentum
    • Atomic spectra of alkali metals
    • The Stern-Gerlach Experiment
    • Importance of spin angular momentum in modern physics: the Higgs boson
    • The need for a description of spin angular momentum
  • The Mathematical Description of Spin
    • Linear Vector Spaces
    • Spinors
    • The Pauli Spin Matrices
    • Exercises in Linear Vector Spaces
  • Non-Relativistic Quantum Mechanics
    • The Schroedinger Wave Equation
    • The Wave Function
    • One Spin-1/2 Particle
    • Multi-particle systems and addition of spin angular momentum
    • Addition of total angular momentum
  • Relativistic Quantum Mechanics
    • The Relativistic Wave Equation
    • Spin and the Wave Function
    • Helicity Formalism
  • Spin and the Higgs Boson
    • Models of angular distributions for different spin hypotheses
    • Simulated distributions of angular quantities
    • Experimental distributions of angular quantities
    • Determining the spin of the Higgs candidate