In this course, world renowned physicist, Leonard Susskind, dives into the fundamentals of classical mechanics and quantum physics. He discovers the link between the two branches of physics and ultimately shows how quantum mechanics grew out of the classical structure. In this lecture, he discusses some of the basic logic in quantum mechanics and then moves into some more mathematical concepts. Professor Susskind introduces the simplest possible quantum mechanical system: a single particle with spin. He presents the fundamental logic of quantum mechanics in terms of preparing and measuring the direction of the spin. This fundamental logic differs from classical systems in that it is entirely about probabilities, and therefore is very different from classical boolean logic. Professor Susskind then reviews the concept of vector spaces and describes the vector space for a single spin system. He concludes the lecture by relating the concept of orthogonality in vector spaces to overlaps in configuration or phase space. More precisely orthogonal vector space states correspond to a lack of overlap in configuration space. Topics: - Single spin system - Basic logic of quantum mechanics - Vector spaces - Basis vectors - Analogy between vector space and configuration space Recorded on January 16, 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.