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: tmpchemistry@gmail.com

— 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