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Physics 452

Physics 452. Quantum mechanics II Winter 2012. Karine Chesnel. Phys 452. Announcements. Tuesday Jan 31 Homework # 7 Pb 6.23, 6.24, 6.25, 6.27, 6.28. Mid-term Exam I When: Fri Feb 3 – Mon Feb 6 Where: testing center. Wed Feb 1: Review continued Friday Feb 3: NO CLASS. Phys 452.

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Physics 452

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  1. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

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

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

  4. Phys 452 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

  5. Phys 452 Review I What to remember?

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

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

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

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

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

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

  12. Phys 452 Equivalent to solve: Degenerate perturbation theory Two-fold degeneracy E d=2 E0

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

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

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

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

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

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

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

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

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

  22. Phys 452 Hyperfine splitting Two-particles system: E • First observed in 1881 by Michelson • Explained in 1924 by Pauli • Radiation • omnipresent • in the interstellar • medium Microwave - radiowave Sp Se Bp electron: e- , me Proton: e+, mp

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