CHEM 4502 Lecture Notes - Lecture 11: Hermite Polynomials, Linear Independence, Harmonic Oscillator
Document Summary
We"re going to sovle schrodinger eqn for harmonic oscillator to learn about molecular vibrations. Each atom"s motion is described by motion in 3 dimensions. Molecule translate (whole molecule moves) rotate vibration linear (all atoms in a line) 3 degrees of freedom nonlinear (like water) 3n - 6 ex: azopyridine molecules vibrates at 1573 cm-1 for c=c stretches (21 fs) lower energy vibration at 46 cm-1, torsional mode (724 fs) Ch stretches are high energy 3122 cm-1 b/c h"s are light (10 fs) the higher the energy, the faster the time. There are 3n - 5 (for linear molecules) or 3n - 6 (for nonlinear molecules) vibrations, where n = the number of atoms in the molecule. That"s a lot, so we will start more simply. Let"s approximate a single ch stretching vibration as a ball on a spring attached to a big heavy wall eqbm position.
