1. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

2. Mid-term Exam I When: Fri Feb 3 – Mon Feb 6 Where: testing center Wed Feb 1: Review continued Friday Feb 3: NO CLASS Tuesday Jan 31 Homework # 7 Pb 6.23, 6.24, 6.25, 6.27, 6.28 Announcements Phys 452

3. EXAM I Time limited: 3 hours Closed book Closed notes Useful formulae provided Review lectures, Homework and sample test Phys 452

4. EXAM I 1. Quantum Statistical Mechanics 2. Non-degenerate perturbation theory 3. Degenerate perturbation theory 4. Fine structure of hydrogen atom 5. Zeeman effect / Hyperfine splitting Phys 452

5. Review I What to remember? Phys 452

6. Quantum statistical mechanics Phys 452 Most probable occupation number: Identical fermions Distinguishable particle Identical bosons Fermi- Dirac statistic Bose-Einstein statistic Maxwell-Boltzmann statistic

7. Quantum statistical mechanics Phys 452 Fermi-Dirac distribution: if

8. Quantum statistical mechanics Phys 452 Black-body spectrum Photons Boson: S=1; m=+/-1 Energy- wavelength: Non-conservation of number of photons

9. Perturbation theory Phys 452 Unperturbed states Building the true states and true energies to some order zero- order first- order second- order

10. Non-degenerate Perturbation theory First-order correction Phys 452 Energy State

11. Non-degenerate Perturbation theory Second-order correction Phys 452 Energy Only works if the energies are non-degenerate

12. Degenerate perturbation theory Phys 452 Two-fold degeneracy E E0E0 d=2 Equivalent to solve:

13. Degenerate perturbation theory Phys 452 Higher –order degeneracy Find eigenvalues of d = 3 3 energies d = N Find eigenvalues of N energies

14. Degenerate perturbation theory Phys 452 General method Start with an ortho-normal basis of the unperturbed states If the state is degenerate: build Diagonalize W : the eigenvalues are If the state is non-degenerate:

15. Phys 452 The fine structure of hydrogen Motion of the electron Coulomb interaction between e - and nucleus Bohr’s energies

16. Phys 452 The fine structure of hydrogen Bohr’s energy E = Relativistic correction + Fine structure Spin-orbit coupling + S “ Classical view” B e+e+ e-e-

17. Phys 452 The fine structure of hydrogen Bohr’s energy E = Relativistic correction + Fine structure Spin-orbit coupling +

18. Phys 452 The fine structure of hydrogen Bohr’s energy E = New relevant quantum numbers: n, l, s, j and m j + Zeeman effect+ Fine structure ?

19. Phys 452 Zeeman effect “Classical view” e-e- S L B ext Weak-field Strong field Intermediate field Fine structure dominates Zeeman effect dominates Comparing:and

20. Phys 452 Zeeman effect Weak -field e-e- S L B ext Good eigenstates: with Lande factor:

21. Phys 452 Zeeman effect e-e- S L B ext Strong -field Good eigenstates:

22. Phys 452 Hyperfine splitting E Microwave - radiowave First observed in 1881 by Michelson Explained in 1924 by Pauli Radiation omnipresent in the interstellar medium Proton: e +, m p electron: e -, m e SeSe BpBp SpSp Two-particles system: