Quantum Chemistry and Spectroscopy - Quantum Chemistry 4.14 - Time Dependence

Short lecture on the time dependence of wavefunctions. Wavefunctions are solutions to the time-dependent Schrodinger equation (TDSE). The superposition principle states that we can express the wavefunction as a superposition of the eigenfunctions of the Hamiltonian operator. These eigenfunctions do not change expectation values over time, and are referred to as stationary states. Separation of variables allows us to show that the time dependence of individual eigenfunctions is a complex exponential with an angular frequency depending on the energy eigenvalue of the eigenfunction. The interaction of these complex exponentials among all of the stationary states gives rise to oscillation in the system over time. Notes Slide: http://i.imgur.com/Y6SUOZu.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