Fourier Analysis applied to Quantum Mechanics 
Fourier Analysis applied to Quantum Mechanics
by Stanford / Leonard Susskind
Video Lecture 9 of 10
Copyright Information: All rights reserved to Prof. Leonard Susskind, Stanford University.
Not yet rated
Views: 2,535
Date Added: January 11, 2015

Lecture Description

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.

Course Index

Course Description

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.

Comments

There are no comments. Be the first to post one.
  Post comment as a guest user.
Click to login or register:
Your name:
Your email:
(will not appear)
Your comment:
(max. 1000 characters)
Are you human? (Sorry)