Quantum Chemistry and Spectroscopy - Quantum Chemistry 4.15 - Time Dependence Animation

Short demonstration of the time dependence of wavefunctions. The time dependence of the wavefunction is demonstrated for particle in a box wavefunctions. The general solution to the time-dependent Schrodinger equation is a linear combination of the eigenfunctions of the Hamiltonian operator, each multiplied by a complex exponential whose angular frequency is dependent on the energy eigenvalue of that eigenfunction. Individual eigenfunctions form stationary states which do not move over time, but having non-zero coefficients on multiple basis functions results in oscillation and a particle which moves over time with a non-zero momentum. Graph: https://www.desmos.com/calculator/ogqsx8uipx --- 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