Quantum Chemistry and Spectroscopy - Quantum Chemistry 4.13 - Commuting Operators

Short lecture on commuting operators in quantum mechanics. Here we set out to prove that if two operators A and B have the same set of eigenfunctions n, then the commutator of A and B is zero. Using the superposition principle, we can expand the commutator as acting on all of the eigenfunctions of the operators. This results in eigenvalues which are of equal and opposite magnitude, cancelling for each term. Thus any time two operators commute they have a common set of eigenfunctions and can both be measured simultaneously to arbitrarily high precision. The Heiseneberg uncertainty principle arises due to the non-zero commutator of position and momentum. Notes Slide: http://i.imgur.com/U9SFOYO.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: [email protected] --- Video Links --- Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicLLM5kDbCf6ljLKZghgkLh4 Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicL3jKr_0nHHs5TwfhdkMFhh Course Review: https://www.youtube.com/playlist?list=PLm8ZSArAXicLTRn3cJyyU1TiU7n_Pp4X1 Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8