Quantum Chemistry and Spectroscopy - Quantum Chemistry 7.4 - Hydrogen Atom Total Wavefunctions

Short lecture on hydrogen atom total wavefunctions. The wavefunctions of the hydrogen atom quantum mechanical model system are a product of the radial wavefunctions and the angular wavefunctions. The radial wavefunctions are a product of a normalization constant, the associated Laguerre polynomials, and a decaying exponential in r. The angular wavefunctions are the spherical harmonics, which are equivalent to the rigid rotor wavefunctions in theta and phi. The quantum number n is the principal quantum number, which starts at 1 and goes to infinity. It determines the energy of the orbital (1s, 2s, 3s, etc.) with an inverse quadratic dependence. The quantum number L goes from zero to n-1, and determines the shape of the orbital (s=0, p=1, d=2, etc.). The quantum number m goes from -L to +L and determines the orientation of the orbital (px vs. py vs. pz, etc.). Combined these quantum numbers and wavefunctions determine the value of the electron probability density at any location in 3-D space. Notes Slide: http://i.imgur.com/nA4HC5v.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=PLm8ZSArAXicLqbzYEN863Fuf73poOW1US 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