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

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Presentation transcript:

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

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

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

Periodic table Quantum mechanics Filling the shells

Periodic table Quantum mechanics Spectroscopic symbol

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

Periodic table Quantum mechanics

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

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

Periodic table Quantum mechanics Filling the shells

Quantum mechanics

Periodic table Quantum mechanics Spectroscopic symbol

Periodic table Quantum mechanics

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

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

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

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

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

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

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

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

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

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 ?

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

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

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

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

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