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 opens the lecture by presenting the four fundamental principles of quantum mechanics that he touched on briefly in the last lecture. He then discusses the evolution in time of a quantum system, and describes how the classical concept of reversibility relates to the quantum mechanical principle of conservation of information, which is actually the conservation of distinctions or distinguishability of states. The evolution in time of a quantum system is represented by unitary operators which preserve distinctions and overlap.
Professor Susskind then derives the timedependent Schrödinger equation, and describes how to calculate the expected value of an observable, and how it changes with time. This discussion introduces the commutator operator. Professor Susskind closes the lecture by showing the connection between the quantum mechanical commutator and the Poisson bracket formulation of classical physics, thus showing how the time evolution of the expected value of an observable is closely related to classical equations of motion.
 Four fundamental principles of quantum mechanics
 Unitarity and unitary evolution of a system
 Reversibility, conservation of information, preservations of distinctions, and conservation of overlap of states
 Derivation of the timedependent Schrödinger equation
 Time evolution of expectation value and equivalence to classical equations of motion
 Parallel between quantum mechanical commutator and classical Poisson bracket