1. Lecture 4. Application to the Real World Particle in a “Finite” Box (Potential Well) Tunneling through a Finite Potential Barrier
References
Engel, Ch. 5
Molecular Quantum Mechanics, Atkins & Friedman (4th ed. 2005), Ch. 2.9
Introductory Quantum Mechanics, R. L. Liboff (4th ed, 2004), Ch. 7-8
A Brief Review of Elementary Quantum Chemistry
Wikipedia ( Search for
Finite potential well
Finite potential barrier
Quantum tunneling
Scanning tunneling microscope

2. Wilson Ho (UC Irvine)

3. PIB Model for -Network in Conjugated Molecules
LUMO 
375 nm
HOMO

4. (Engel, C5.1)
1,3,5-hexatriene
LUMO
375 nm
HOMO

5. Calculation done by Yoobin Koh

6. Origin of Color: -carotene

8. Origin of Color: chlorophyll

9. Solar Spectrum (Irradiation vs. Photon Flux)
Maximum photon flux of the solar ~ 685 nm

10. Solar Spectrum (Irradiation vs. Photon Flux)

11. Understanding & Mimicking Mother Nature
for Clean & Sustainable Energy:
Artificial Photosynthesis

12. Organic Materials for Solar Energy Harvesting
Bulk heterojunction solar cell
with a tandem-cell architecture
Hou, et al., (2008) Macromolecules
Hole
Electron
Charge
Separation
Donor polymer
acceptor

13. Essentially no thermal excitation Boltzmann Distribution
(Engel, Section 2.1, P.5.2)

14. Particle in a finite height box: a potential well V(x)II
III
 is not required to be 0 outside the box.

15. Particle in a finite height box (bound states: E < V0)
(1) the Schrödinger equation I II
III
 is not required to be 0 outside the box.
(2) Plausible wave functions
(3) Boundary conditions 
-a/2
a/2

16. Particle in a finite height box: boundary condition III
III 
(Engel, P5.7)

17. Particle in a finite height box: boundary condition II
(4) the final solutions
Region III
Region I
Region II
-a/2
a/2 I II
III
1.07
0.713
0.409
0.184
0.0461
(Engel, P5.7)

18. Particle in a finite height box: the final solutions
tan
(Example) V0 = 1.20 x J, a = 1.00 nm E2
0.184 E4
0.713 E1
0.0461 E3
0.409 E5
1.07

19. Tunneling to classically-forbidden region

20. .

21. valence
electrons
core
electrons

22. From two to infinite array of Na atoms

24. Tunneling through a finite potential barrier
(or U)
(or L)

25. P5.1 8

26. Tunneling through a finite potential barrier
Inside the barrier
Outside the barrier
Define alpha and represent equation
Define k and represent equation

27. Tunneling through a finite potential barrier
Inside the barrier
Outside the barrier Ⅰ Ⅱ Ⅲ
Assume that electrons are moving left to right.
Boundary conditions
Ⅰ / Ⅱ Ⅱ Ⅰ
Ⅱ / Ⅲ Ⅲ

28. Transmission coefficient
4 equations for 4 unknowns. Solve for T.
barrier width
(decay length)-1

29. Probability current density (Flux)

30. Scanning Tunneling Microscope (STM)
applications
Scanning Tunneling Microscope (STM)
Introduced by G. Binnig and W. Rohrer at the IBM Research Laboratory in 1982 (Noble Prize in 1986)
Basic idea
Electron tunneling current depends on the barrier width and decay length.
STM measures the tunneling current to know the materials depth and surface profiles.

32. Modes of Operation Constant Current Mode
Tips are vertically adjusted along the constant current 
Constant Height Mode
Fix the vertical position of the tip
Barrier Height Imaging
Inhomogeneous compound
Scanning Tunneling Spectroscopy
Extension of STM this mode measured the density of electrons in a sample

34. Quantum dot / Quantum well

35. How to put an elephant in a fridge? QM version no. 2

36. How to put an elephant in a fridge? QM version no. 2
냉장고 문을 닫는다.
코끼리가 냉장고를 향해 돌진한다.
이 과정을 반복하면 양자터널링 현상에 의해 언젠가는 코끼리가 냉장고에 들어간다.
Close the fridge door.
Make the elephant run to the fridge.
Repeating this for infinite times, the elephant will eventually enter the fridge through the door (by quantum tunneling).