Quantum Chemistry and Spectroscopy - Quantum Chemistry 6.12 - Angular Momentum Eigenvalues

Short lecture on the eigenvalues of rigid rotor wavefunctions. The Hamiltonian operator of the rigid rotor quantum mechanical model system can be expressed in terms of the total angular momentum squared operator. Thus, the rigid rotor wavefunctions (spherical harmonics) are eigenfunctions of the total angular momentum squared operator, with an eigenvalue of [ hbar^2 J(J+1) ]. Additionally, these wavefunctions are eigenfunctions of the z-component angular momentum operator Lz, with an eigenvalue of [ hbar m ]. These wavefunctions are not eigenfunctions of Lx or Ly. Notes Slide: http://i.imgur.com/lVMqzKR.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=PLm8ZSArAXicIlRL7FdtY3GjmKju4ORHIs 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