Quantum Chemistry and Spectroscopy - Quantum Chemistry 5.11 - 3-D Harmonic Oscillator

Short lecture on the three dimensional harmonic oscillator. The three dimensional harmonic oscillator has a quadratic potential energy function in three dimensions (x, y, and z) each with their own spring constants. This potential energy function (and thus the Hamiltonian) can be factored into an independent function in each dimension, solving the Schrodinger equation through separation of variables. The result is a total energy which is a sum of the harmonic oscillator energy in each of the three dimensions. If the springs constants are equal, this leads to a symmetry which causes degeneracy in much the same fashion as in the three dimensional particle in a box. Notes Slide: http://i.imgur.com/2B34SPX.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=PLm8ZSArAXicL4kdvchwcgETYWXlt-HyzH 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