Quantum Chemistry and Spectroscopy - Quantum Chemistry 5.5 - Harmonic Oscillator Energy Levels

Short lecture on the energy levels of the quantum harmonic oscillator. The vibrations of diatomic molecules can be modeled using the harmonic oscillator model system which approximates the electronic potential energy surface as a parabola with a minimum at the equilibrium bond length. Solving the Schrodinger equation for the harmonic oscillator potential produces a set of distinct wavefunctions and energy levels. The energy levels depend on the spring constant, and the reduced mass of the two atoms of the molecule. The quantum number n starts at zero and goes up to infinity as an integer. The lowest energy state has a non-zero "zero-point vibrational energy" (ZPVE). All subsequent energy levels are evenly spaced. Notes Slide: http://i.imgur.com/hl1Fm5E.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