Lecture Playlist

Introduction to quantum mechanics

The basic logic of quantum mechanics

Vector spaces and operators

Time evolution of a quantum system

Uncertainty, unitary evolution, and the Schrödinger equation

Entanglement

Entanglement and the nature of reality

Particles moving in one dimension and their operators

Fourier analysis applied to quantum mechanics and the uncertainty principle

The uncertainty principle and classical analogs
Professor Susskind begins the lecture by introducing the Heisenberg uncertainty principle and explains how it relates to commutators. He proves that two simultaneously measurable operators must commute. If they don't then the observables corresponding to the two operators cannot be measured simultaneously.
He then reviews the time evolution of a system and the Schrödinger equation. Unitary operators represent the time evolution of a system, and the quantum mechanical Hamiltonian generates the time evolution. Professor Susskind reviews the derivation of the timedependent Schrodinger equation, the computation of expectation values of observables, and the parallels between the quantum mechanical commutator and the classical Poisson bracket.
Professor Susskind then demonstrates how to solve the Schrödinger equation for a general quantum mechanical system. This solution is the origin of the connection between the energy of a system and oscillations of the wave function. This is the Heisenberg matrix formulation of quantum mechanics.
The lecture concludes by solving a practical example of a single spin in a constant magnetic field.
 Pure states
 Heisenberg uncertainty principle
 Commutator
 Time evolution of a system
 Quantum mechanical Hamiltonian
 Timedependent Schrödinger equation
 Solving the Schrödinger equation
 Expectation values of observables
 Heisenberg's matrix formulation of Quantum Mechanics
 Spin in a magnetic field