Quantum Chemistry and Spectroscopy - Quantum Chemistry 3.7 - Particle in a Box Wavefunction Plots

Short lecture demonstrating particle in a box wavefunctions. The particle in a box is a quantum mechanical model system for a particle which is restricted to a finite region of space. The potential energy is zero inside the box (zero to L) and infinite outside. The energy levels depend quadratically on a quantum number n [ E_n = h^2 n^2 / (8 m L^2) ] which is between 1 and infinity (n = 1, 2, 3, ...). The wavefunction is a half-integer number of sine waves inside the box [ psi_n(x) = sqrt(2 / L) sin(n pi x / L) ]. Quantum behavior disappears when you go to sufficiently large values of box length L and/or particle mass m. Graph: https://www.desmos.com/calculator/zqo7bncevb --- 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=PLm8ZSArAXicL6ArmHxHxgugNNsSYYD3MW 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