p3316 spring2009 lecture20 - cornell universityliepe/webpage/docs/p3316... · 2010-05-06 ·...
TRANSCRIPT
![Page 1: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/1.jpg)
-5 0 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x
E/ h
ωω ωωV(x)En
ψψψψ(x)
Lecture 20: 03/04/09
Numerical solution of Schrödinger's Equation
![Page 2: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/2.jpg)
II2,5 The simple harmonic oscillator potential V(x)=1/2cx 2:
-5 0 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x
E/ h
ωω ωω
V(x)Enψψψψ(x)
![Page 3: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/3.jpg)
![Page 4: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/4.jpg)
![Page 5: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/5.jpg)
![Page 6: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/6.jpg)
-5 0 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x
E/ h
ωω ωω
-5 0 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x
E/ h
ωω ωω
V(x)En
ψψψψ (x)
V(x)En
|ψψψψ (x)|2
![Page 7: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/7.jpg)
Atomic molecule vibrationAtomic molecule vibration
Near equilibrium: simple harmonic ωh)2
1( += nEn
21
21
mm
mm
+=µ
reduced mass, µµµµ
![Page 8: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/8.jpg)
Example: CO2
![Page 9: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/9.jpg)
Molecule vibration and rotation:
![Page 10: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/10.jpg)
Example: H2O
![Page 11: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/11.jpg)
II2,6 Numerical Solution of the time-indep. Schrödinger E qu.:
![Page 12: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/12.jpg)
![Page 13: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/13.jpg)
![Page 14: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/14.jpg)
![Page 15: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/15.jpg)
![Page 16: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/16.jpg)
![Page 17: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/17.jpg)
![Page 18: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/18.jpg)
![Page 19: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/19.jpg)
![Page 20: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/20.jpg)
![Page 21: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/21.jpg)
![Page 22: P3316 spring2009 lecture20 - Cornell Universityliepe/webpage/docs/P3316... · 2010-05-06 · P3316_spring2009_lecture20 Author: admin Created Date: 3/4/2009 12:00:00 AM](https://reader034.vdocuments.mx/reader034/viewer/2022043009/5f9d42dfdfee503952611470/html5/thumbnails/22.jpg)