8. One-Dimensional Wave Functions

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.

00:00 - Chapter 1. Review: The Curvature of the Wave Function and Kinetic Energy
06:44 - Chapter 2. Relationships between Nodes and Curvature of the Wave Function
23:49 - Chapter 3. The Square of Psi as the Probability Density
31:46 - Chapter 4. Constraints of Energy in the Harmonic Oscillator, the Morse Potential and the Coulombic Potential
42:12 - Chapter 5. The Influence of Mass on Bond Dynamics, Strength, and Distance

Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses

This course was recorded in Fall 2008.

Category:

Education

Tags:

• Schrödinger equation
• wave function
• negative kinetic energy
• curvature
• nodes