Lecture 8: One-Dimensional Wave Functions (CHEM 125a)
This lecture explores the curvature of wave functions as it relates to kinetic energy and electron probability density, demonstrating how non-divergence mandates quantized energy levels for harmonic oscillator, Morse, and Coulombic potentials. It further examines the 'isotope effect' on bond dynamics and energy.
Freshman Organic Chemistry (CHEM 125)
Professor McBride expands on the recently introduced concept of the wave function by illustrating the relationship of the magnitude of the curvature of the wave function to the kinetic energy of the system, as well as the relationship of the square of the wave function to the electron probability density. The requirement that the wave function not diverge in areas of negative kinetic energy leads to only certain energies being allowed, a property which is explored for the harmonic oscillator, Morse potential, and the Columbic potential. Consideration of the influence of mass reveals an "isotope effect" on dynamics, on the energy, vibration frequency, and length of bonds.
7. Quantum Mechanical Kinetic Energy
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