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H = ½ω(p2 + q2)
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 = ax2
The Quadratic Curve
Harmonic Oscillator
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
Hooke
F = -kx
Anharmonic Oscillator
Born and Oppenheimer
Born-Oppenheimer Theory
E= i Ei
Born Oppenheimer Separation
Separation Vibration Rotation
Born Oppenheimer Separation Vib - Rot
Harry Kroto 2004
Vibration Rotation Spectroscopy
CO Infra Red Spectrum (Colin)
ABC Rotation of a Diatomic Molecule
CO Rotational Spectrum PROBLEM
Hamilton
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