Building on the previous discussion of atomic energy levels, Leonard Susskind demonstrates the origin of the concept of electron spin and the exclusion principle.

Professor Susskind builds on the discussion of quantum harmonic oscillators from the last lecture to derive the higher order energy states and wave functions. He then moves on to discuss spin states of particles, and introduces the Pauli matrices, which account for the interaction of a particle's spin with an external magnetic field. By examining the energy levels of electrons in an atom, Pauli and others realized that only two electrons can be in any given state. This led both to the the exclusion principle, as well as the need for another state variable - spin - which allows two electrons in each energy level.

Recorded on October 14, 2013.

1. Review of quantum mechanics and introduction to symmetry
2. Symmetry groups and degeneracy
3. Atomic orbits and harmonic oscillators
4. Spin, Pauli Matrices, and Pauli Exclusion Principle
5. Fermions: a tale of two minus signs
6. Quantum Field Theory: Particle Creation and Annihilation Operators
7. Quantum Field Theory: Fermions and Bosons
8. Second Quantization
9. Quantum Field Hamiltonian
10. Fermions and the Dirac equation

This course will explore the various types of quantum systems that occur in nature, from harmonic oscillators to atoms and molecules, photons, and quantum fields. Students will learn what it means for an electron to be a fermion and how that leads to the Pauli exclusion principle. They will also learn what it means for a photon to be a boson and how that allows us to build radios and lasers. The strange phenomenon of quantum tunneling will lead to an understanding of how nuclei emit alpha particles and how the same effect predicts that cosmological space can “boil.” Finally, the course will delve into the world of quantum field theory and the relation between waves and particles.