After a brief review of the prior Quantum Mechanics course, Leonard Susskind introduces the concept of symmetry, and present a specific example of translational symmetry.

The course begins with a brief review of quantum mechanics and the material presented in the core Theoretical Minimum course on the subject. The concepts covered include vector spaces and states of a system, operators and observables, eigenfunctions and eigenvalues, position and momentum operators, time evolution of a quantum system, unitary operators, the Hamiltonian, and the time-dependent and independent Schrodinger equations.

After the review, Professor Susskind introduces the concept of symmetry. Symmetry transformation operators commute with the Hamiltonian. Continuous symmetry transformations are composed from the identity operator and a generator function. These generator functions are Hermitian operators that represent conserved quantities.

The lecture closes with the example of translational symmetry. The generator function for translational symmetry is the momentum operator divided by ħ.

Recorded on September 23, 2013.

Topics:
- Vector space
- Observables
- Hermitian operators
- Eigenvectors and eigenvalues
- Position and momentum operators
- Time evolution
- Unitarity and unitary operators
- The Hamiltonian
- Time-dependent and independent Schrödinger equations
- Symmetry
- Conserved quantities
- Generator functions

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.