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H = ½ ω (p 2 + q 2 )

H = ½ ω (p 2 + q 2 ). The Harmonic Oscillator QM. Recap of the Rotational and Vibrational Energy Level Expressions for a Rigid Diatomic Molecule Vibrating with Simple Harmonic Motion. Recap Rot & Vib Energy Level. y = ax 2. The Quadratic Curve. Harmonic Oscillator.

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H = ½ ω (p 2 + q 2 )

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  1. H = ½ω(p2 + q2) The Harmonic Oscillator QM

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

  3. y = ax2 The Quadratic Curve

  4. Harmonic Oscillator

  5. A Classical Description E = T + V E = ½mv2 + ½kx2 B QM description - the Hamiltonian H v = E(v) v C Solve the Hamiltonian - Energy Levels G(v) = ω(v+ ½) (cm-1) D Selection Rules - Allowed Transitions v =±1 E Transition Frequencies > G = ω F Intensities - THE SPECTRUM J Analysis - Pattern recognition; assign quantum numbers H Experimental Details - spectrometers, lasers I More Advanced Details: anharmonicity J Information: potential, force constants, group identification Harry Kroto 2004

  6. F = -kx Hooke

  7. Anharmonic Oscillator

  8. Born and Oppenheimer

  9. E= i Ei Born-Oppenheimer Theory

  10. Born Oppenheimer Separation

  11. Separation Vibration Rotation

  12. Born Oppenheimer Separation Vib - Rot

  13. Vibration Rotation Spectroscopy Harry Kroto 2004

  14. CO Infra Red Spectrum (Colin)

  15. ABC Rotation of a Diatomic Molecule

  16. CO Rotational Spectrum PROBLEM

  17. Hamilton

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