Quantum Chemistry and Spectroscopy - Quantum Chemistry 4.10 - Superposition Principle 1: Basis Sets

Short lecture on the superposition principle in quantum mechanics. The superposition principle says that in general any wavefunction can be expressed as a linear combination of the set of eigenfunctions of the Hamiltonian operator for a system. The set of eigenfunctions form the basis set, which are added together with various complex coefficients. Any function which can be represented as such a linaer combination is said to be in the space of the basis set. The resolution of the identity operator can be used to "transform" a function between representations in different basis sets. If the resolution of the identity is equivalent to an identity operator, then the basis set is said to be "complete". Notes Slide: http://i.imgur.com/We2mvj1.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=PLm8ZSArAXicLLM5kDbCf6ljLKZghgkLh4 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