Leonard Susskind diverges from looking at the theory behind quantum mechanics and shifts the focus toward looking at more tangible examples. He opens the lecture with a review of the entangled singlet and triplet states and how they decay. He then shows how Fourier analysis can be used to decompose a typical quantum mechanical wave function. He then continues the discussion of a continuous system - a single particle moving in one dimension - and shows that the solutions to the eigenvector equations for position and momentum lead to the uncertainty principle. In other words, the wave function solution for a specific value of momentum has probabilities for the position everywhere (in the single dimension). This derivation shows that the position and momentum wave functions are Fourier transforms of each other. Thus mathematically the uncertainty principle is simply a a statement about Fourier transforms. Topics: - Triplet state decay - Fourier analysis applied to quantum mechanics - Relationship between the Fourier transform and the uncertainty principle Recorded on February 27, 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.