Leonard Susskind discusses an array of topics including uncertainty, the Schrödinger equation, and how things evolve with time. He 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 time-dependent Schrödinger 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. Topics: - Pure states - Heisenberg uncertainty principle - Commutator - Time evolution of a system - Quantum mechanical Hamiltonian - Time-dependent Schrödinger equation - Solving the Schrödinger equation - Expectation values of observables - Heisenberg's matrix formulation of Quantum Mechanics - Spin in a magnetic field Recorded on February 6, 2012.

1. Introduction to Quantum Mechanics
2. The Basic Logic of Quantum Mechanics
3. Vector Spaces and Operators
4. Time Evolution of a Quantum System
5. Heisenberg Uncertainty Principle & The Schrödinger Equation
6. Entanglement: Entangled, Singlet, & Triplet States
7. Entanglement and the Nature of Reality
8. Particles Moving in One Dimension and their Operators
9. Fourier Analysis applied to Quantum Mechanics
10. The Uncertainty Principle and Classical Analogs

Quantum theory governs the universe at its most basic level. In the first half of the 20th century physics was turned on its head by the radical discoveries of Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, and Erwin Schroedinger. An entire new logical and mathematical foundation—quantum mechanics—eventually replaced classical physics. We will explore the quantum world, including the particle theory of light, the Heisenberg Uncertainty Principle, and the Schrödinger Equation. This course is second-part of a six course sequence given by Prof. Leonard Susskind that explores the theoretical foundations of modern physics - the Theoretical Minimum. Topics in the series include classical mechanics, quantum mechanics, theories of relativity, electromagnetism, cosmology, and black holes.