Quantum Chemistry and Spectroscopy - Quantum Chemistry 4.11 - Superposition Principle 2: Expectation Values

Short lecture on the superposition principle in quantum mechanics. The superposition principle states that a general wavefunction can be expressed as a linear combination of the eigenfunctions of the Hamiltonian operator. If the basis set of eigenfunctions are orthonormal, then the sum of the square magnitude of all coefficients must be one to normalize the wavefunction. The expectation value of the total energy is the sum over all basis functions of their square coefficient times their energy eigenvalue. The probability of measuring each energy eigenvalue during measurement is equal to the square magnitude of the coefficient for that basis function. Notes Slide: http://i.imgur.com/65bsi5A.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