LECTURE 11 SPINS

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

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.

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:

Determining Operator S2 Determine Sz using similar technique.

Sx and Sy Pauli Spin Matrices

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.

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 =

Problem

Problem 1 10

Problem 2

Problem 3 12

Problem 3