H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.
-
Upload
junior-butler -
Category
Documents
-
view
224 -
download
1
Transcript of H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.
![Page 1: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/1.jpg)
H = ½ω(p2 + q2)
The Harmonic Oscillator QM
![Page 2: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/2.jpg)
![Page 3: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/3.jpg)
Recap of the Rotational and Vibrational Energy Level Expressions for a Rigid
Diatomic Molecule Vibrating with Simple Harmonic Motion
Recap Rot & Vib Energy Level
![Page 4: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/4.jpg)
![Page 5: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/5.jpg)
y = ax2
The Quadratic Curve
![Page 6: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/6.jpg)
![Page 7: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/7.jpg)
Harmonic Oscillator
![Page 8: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/8.jpg)
![Page 9: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/9.jpg)
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
![Page 10: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/10.jpg)
![Page 11: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/11.jpg)
Hooke
F = -kx
![Page 12: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/12.jpg)
![Page 13: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/13.jpg)
Anharmonic Oscillator
![Page 14: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/14.jpg)
![Page 15: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/15.jpg)
Born and Oppenheimer
![Page 16: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/16.jpg)
Born-Oppenheimer Theory
E= i Ei
![Page 17: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/17.jpg)
Born Oppenheimer Separation
![Page 18: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/18.jpg)
Separation Vibration Rotation
![Page 19: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/19.jpg)
![Page 20: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/20.jpg)
Born Oppenheimer Separation Vib - Rot
![Page 21: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/21.jpg)
![Page 22: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/22.jpg)
Harry Kroto 2004
Vibration Rotation Spectroscopy
![Page 23: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/23.jpg)
CO Infra Red Spectrum (Colin)
![Page 24: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/24.jpg)
ABC Rotation of a Diatomic Molecule
![Page 25: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/25.jpg)
CO Rotational Spectrum PROBLEM
![Page 26: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/26.jpg)
Hamilton
![Page 27: H = ½ ω (p 2 + q 2 ) The Harmonic Oscillator QM.](https://reader036.fdocument.pub/reader036/viewer/2022062314/5697bf771a28abf838c818a9/html5/thumbnails/27.jpg)