Quantum Chemistry and Spectroscopy - Quantum Chemistry 5.8 - Harmonic Oscillator Wavefunctions

Short lecture on the harmonic oscillator wavefunctions. The harmonic oscilllator wavefunctions are the eigenfunctions of a one dimensional Hamiltonian operator with a quadratic potential energy function. The wavefunctions depend on a (positive integer) quantum number which starts at 1 as well as the spring constant and reduced mass of the diatomic molecule. The three components of each wavefunction are a normalization constant, a Gaussian function, and a Hermite polynomial of equal order to the quantum number n. Hermite polynomials may be determined from a generating function or looked up in a table. Graph: https://www.desmos.com/calculator/cfm7kfqgeu Notes Slide: http://i.imgur.com/tShBa6X.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