Lecture Playlist

Review of quantum mechanics and introduction to symmetry

Introduction to quantum mechanics

Symmetry groups and degeneracy

The basic logic of quantum mechanics

Atomic orbits and harmonic oscillators

Vector spaces and operators

Spin

Time evolution of a quantum system

Fermions: a tale of two minus signs

Uncertainty, unitary evolution, and the Schrödinger equation

Quantum field theory

Entanglement

Quantum field theory 2

Entanglement and the nature of reality

Particles moving in one dimension and their operators

Second quantization

Fourier analysis applied to quantum mechanics and the uncertainty principle

Quantum field Hamiltonian

The uncertainty principle and classical analogs

Fermions and the Dirac equation
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 timedependent 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.
 Vector space
 Observables
 Hermitian operators
 Eigenvectors and eigenvalues
 Position and momentum operators
 Time evolution
 Unitarity and unitary operators
 The Hamiltonian
 Timedependent and independent Schrödinger equations
 Symmetry
 Conserved quantities
 Generator functions