1. LECTURE 11
SPINS

2. Spin In Classical Mechanics: Orbital Angular Momentum:
Motion of centre of mass.
Spin:
Motion about centre of mass.
Elementary Particles:
Intrinsic Angular Momentum
Extrinsic Angular Momentum
For angular momentum:
Spin: Fundamental Commutation Relations
Eigenvectors for S2 and Sz

3. Spin Pi meson: s=0 Electrons: s = ½ Photons: s = 1 Deltas: s = 3/2
Gravitons: s = 2
Angular momentum quantum number can take any integer, l.
Spin, s is fixed for any particle.

4. Spin 1/2
Spin of particles that make all ordinary matter: protons, electrons and neutrons as well as quarks and all leptons.
Two eigenstates: Spin up
Spin down
Spinors
s =1/2:

5. Determining Operator S2
Determine Sz using similar technique.

6. Sx and Sy
Pauli Spin Matrices

7. Eigenspinors of Sz If Sz is measured on a particle in a general state
is the probability of getting Sz =
is the probability of getting Sz =
The spinors must be normalized.

8. Eigenspinors of Sx The normalized eigenspinors for Sx
If Sx is measured on a particle in a general state
The probability of getting Sx =
The probability of getting Sx =

9. Problem

10. Problem 1 10

11. Problem 2

12. Problem 3 12

13. Problem 3