1. Physics 451 Quantum mechanics I Fall 2012 Nov 30, 2012 Karine Chesnel

2. Test 3 Last day Today! Quantum mechanics HW 23 Tuesday Dec 4 HW 24 Thursday Dec 6 Homework

3. Periodic table Quantum mechanics Filling the shells 226 s: “sharp” p: “principal” d: “diffuse” f: “fundamental”

4. Periodic table Quantum mechanics Filling the shells

5. Periodic table Quantum mechanics Spectroscopic symbol

6. Periodic table Quantum mechanics Hund’s rules First rule: seek the state with highest possible spin S (lowest energy) Second rule: for given spin S, the state with highest possible angular momentum L has lowest energy Third rule: If shell no more than half filled, the state with J=IL-SI has lowest energy If shell more than half filled, the state with J=L+S has lowest energy

7. Periodic table Quantum mechanics

8. Quiz 31 Quantum mechanics What is the spectroscopic symbol for Silicon ? A. B. C. D. E. Si: (Ne)(3s) 2 (3p) 2

9. Periodic table Quantum mechanics Filling the shells 226 s: “sharp” p: “principal” d: “diffuse” f: “fundamental”

10. Periodic table Quantum mechanics Filling the shells

11. Quantum mechanics

12. Periodic table Quantum mechanics Spectroscopic symbol

13. Periodic table Quantum mechanics

14. Periodic table Quantum mechanics Hund’s rules First rule: seek the state with highest possible spin S (lowest energy) Second rule: for given spin S, the state with highest possible angular momentum L has lowest energy Third rule: If shell no more than half filled, the state with J=L-S has lowest energy If shell more than half filled, the state with J=L+S has lowest energy

15. Quiz 33 Quantum mechanics What is the spectroscopic symbol for Silicon ? A. B. C. D. E. Si: (Ne)(3s) 2 (3p) 2

16. Quiz 33 Quantum mechanics What is the spectroscopic symbol for Chlorine ? A. B. C. D. E. Cl: (Ne)(3s) 2 (3p) 5

17. Solids Quantum mechanics e-e- What is the wave function of a valence electron in the solid?

18. Solids Quantum mechanics e-e- Basic Models: Free electron gas theory Crystal Bloch’s theory

19. Free electron gas Quantum mechanics e-e- e-e- lzlz lyly lxlx Volume Number of electrons:

20. Free electron gas Quantum mechanics e-e- 3D infinite square well 0 inside the cube outside

21. Free electron gas Quantum mechanics e-e- Separation of variables

22. Free electron gas Quantum mechanics Bravais k-space Volume of unit cell

23. Quiz 33c Quantum mechanics A. 1 B. 2 C. q D. Nq E. An infinity How many electrons can be contained in one unit cell in the Bravais k- lattice ?

24. Free electron gas Quantum mechanics Bravais k-space Fermi surface Free electron density

25. Free electron gas Quantum mechanics Bravais k-space Fermi surface Total energy contained inside the Fermi surface

26. Free electron gas Quantum mechanics Bravais k-space Fermi surface Solid Quantum pressure arises from Pauli exclusion principle

27. Solids Quantum mechanics e-e- Bravais k-space Fermi surface Number of unit cells