Quantum Chemistry and Spectroscopy - Quantum Chemistry 4.6 - Commutators

Short lecture on operator commutators in quantum mechanics. The commutator of two operators A and B is the difference between acting on a wavefunction with B then A and A then B. Operators act on a function from right to left. If the commutator of two operators is zero, then A and B are said to "commute". If A and B do not commute, then "uncertainty" exists between the measuring of physical properties A and B. There is an inverse relationship between the uncertainty in one property and the uncertainty in the other. The magnitude of the uncertainty is determined by the Schrodinger-Robertson uncertainty relationship. From this, we can derive the Heisenberg uncertainty principle for position and momentum. Notes Slide: http://i.imgur.com/0fKXddU.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