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Recap of Rotational and Vibrational Energy Levels in Harmonic Oscillator

Reviewing expressions for energy levels of a rigid diatomic molecule vibrating with simple harmonic motion. Compare classical and quantum harmonic oscillator descriptions, solving for energy levels and selection rules for transitions. Analyze spectrum and explore advanced anharmonicity details.

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Recap of Rotational and Vibrational Energy Levels in Harmonic Oscillator

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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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