1. H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM

3. Recap of the Rotational and Vibrational Energy Level Expressions for a Rigid Diatomic Molecule Vibrating with Simple Harmonic Motion Recap Rot & Vib Energy Level

5. y = ax 2 The Quadratic Curve

7. Harmonic Oscillator

9. AClassical Description E = T + V E = ½mv 2 + ½kx 2 B QM description - the Hamiltonian H  v  = E(v)  v  CSolve the Hamiltonian - Energy Levels G(v) = ω(v+ ½) (cm -1 ) DSelection Rules - Allowed Transitions  v = ±1 ETransition Frequencies >  G = ω FIntensities - THE SPECTRUM J Analysis - Pattern recognition; assign quantum numbers HExperimental Details - spectrometers, lasers IMore Advanced Details: anharmonicity JInformation: potential, force constants, group identification Harry Kroto 2004

11. Hooke F = -kx

13. Anharmonic Oscillator

15. Born and Oppenheimer

16. Born-Oppenheimer Theory E=  i E i

17. Born Oppenheimer Separation

18. Separation Vibration Rotation

20. Born Oppenheimer Separation Vib - Rot

22. Harry Kroto 2004 Vibration Rotation Spectroscopy

23. CO Infra Red Spectrum (Colin)

24. ABC Rotation of a Diatomic Molecule

25. CO Rotational Spectrum PROBLEM

26. Hamilton