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### Course information and updated schedule

Course information and updated schedule (29 August 2013)

### Compendium

Compendium, covering QM intro and hydrogen atom

### Compulsory reading, exercises for following lecture, material from lectures

#### Monday, 2 September

Brief presentation of the history of atomic physics & some examples from modern atomic physics

Reading for tomorrow: compendium pp. 1-15

Exercise for tomorrow: For the hydrogen atom show that the classical torque is zero and that the angular momentum is a constant of the motion. What does this mean? Show also that the motion is planar.

#### Tuesday, 3 September

Powerpoint material from the lecture

Reading for tomorrow: compendium pp. 15-30

Exercise for tomorrow: Express the |Sx> vector in terms of the |Sy> vectors. Apply the Sz operator to the |Sx> vectors.

#### Wednesday, 4 September

Reading for tomorrow: compendium pp. 30-42

Exercise for tomorrow: Write down the matrix expression for the Sz operator in the {|Sz,+>,|Sz,->}, {|Sx,+>,|Sx,->}, and {|Sy,+>,|Sy,->} bases.

#### Thursday, 5 September

Reading for Tuesday, 10 September: compendium pp. 42-62

Exercise for Tuesday, 10 September:
• Show [Si,Sj]=i ℏ εijk Sk, where εijk is the Levi-Civita symbol.
• Show {Si,Sj}=1/2 ℏ2 δij.
• Show S2=3/4 ℏ2.
• Show [S2,Si]=0.

#### Tuesday, 10 September

Reading for tomorrow: compendium pp. 62-72

Exercise for tomorrow:

Show that T(dx') = 1-i K dx', with K=(Kx, Ky, Kz) a tuple of Hermitian operators, fulfills the following requirements:
• T(dx') is unitary (conservation of probability),
• T(dx'')T(dx')=T(dx''+dx') (subsequent infinitesimal translations),
• T(dx')=T-1(dx') (reverse translations),
• limdx→0 T(dx')=1 (zero translations).

#### Wednesday, 11 September

Exercise for tomorrow:

Solve the three first tasks after equation (4.28) in the compendium.

#### Thursday, 12 September

Exercise for tomorrow: Solve the remaining tasks on pp. 60 and 61 in the compendium.

#### Friday, 13 September

Reading for Monday: Demtröder sections 5.6 and 5.7.

Exercise for tomorrow: Give an expression for the minimum of the effective potential of the hydrogen atom.

#### Monday, 16 September

Reading for tomorrow: Demtröder section 5.8.

Exercise for tomorrow: Show for the l, s, and j quantum numbers that j ≤ l+s and |l-s| ≤ j, and thus |l-s| ≤ j ≤ l+s.

#### Tuesday, 17 September

Powerpoint material from the lecture

Exercise for tomorrow: calculate the transition matrix element for an optical transition between the hydrogen 1s and 2p states for light with polarisation along the z-axis. Choose the same ml and ms for the initial and final state.

#### Wednesday, 18 September

Reading for tomorrow: Helium atom (e.g. Demtröder 6.1).

#### Thursday, 19 September

Reading for tomorrow: the aufbau principle (e.g. Demtröder 6.2)

Exercise for tomorrow: Convince yourself that the dipole selection rule Δl=±1 implies Δj=0,±1. Then consider the Hα line of the hydrogen emission spectrum (Balmer series, between n=3 and n'=2). Plot all allowed transitions in a Grotrian diagram, taking the fine structure splitting into account, but neglecting hyperfine splitting and Lamb shift. How does the spectrum look like? Don't forget that you have to take the multiplicity of the states into account to get the correct intensities!

#### Friday, 20 September

We started dealing with the helium atom.

No reading, no exercise.

#### Monday, 23 September

We went on with treating the helium atom and started on multi-electron atoms: hamiltonian, central field approximation, aufbau principle.

Powerpoint material from the lecture

#### Monday, 14 October

After some recapitulation of the helium atom (Coulomb and exchange integrals, ) we had a look at the SCF and Hartree-Fock methods, which required introduction of the Slater determinant.

Reading for tomorrow: LS coupling and jj coupling (e.g. Demtröder 6.5)

Written exams from earlier semesters: see above.

#### Tuesday, 15 October

We discussed the non-central part of the potential and compared it in size to the spin-orbit term. Depending on the relative sizes of these terms one either has to consider LS coupling or jj coupling, and we considered both these. In particular we discussed the possible LS-terms for a p2 configuration.

Reading for tomorrow: Vibrations and rotations in molecules (e.g. Demtröder 6.5)

Exercise: Write down the possible terms for a p3 configuration.

#### Wednesday, 16 October

We discussed vibrations in molecules in the harmonic approximation. Then we considered vibrational transitions in infrared absorption and emission and the Raman effect.

#### Thursday, 17 October

We finished off the discussion of the Raman effect and infrared absorption by a comparison of spectra from infrared absorption spectroscopy and Raman spectroscopy. Then we introduced the Morse potential, which gives a more realistic picture of the molecular potential. The vibrational transitions in molecules were discussed on the basis of what is expected for the photoelectric effect.

Exercise: Using the figure below, determine the constant ℏω, ℏω, De, and α for the A 2Π state of carbon monoxide.

#### Thursday, 17 October

We finished off the discussion of the Raman effect and infrared absorption by a comparison of spectra from infrared absorption spectroscopy and Raman spectroscopy. Then we introduced the Morse potential, which gives a more realistic picture of the molecular potential. The vibrational transitions in molecules were discussed on the basis of what is expected for the photoelectric effect.

Exercise: Using the figure below, determine the constant ℏω, ℏω, De, and α for the A 2Π state of carbon monoxide.

### Exam

The written exam will take place on Friday, 25 October.

As a preparation for the exam, you should look at the following things:

• hand-in problems,
• labs,
• practice questions below,
• reading according to the List of subjects and reading suggestions (you *don't* have to read all the books, choose a book that suits you - but remember that you (in principle) have to cover all topics),

In the exam, there will be exercises in which you will be asked to describe a topic (experiment, outline of a theory, physical models, etc.). There will also be exercises where you will have to calculate, similar to what you have done in the hand-in problems, and there will be exercises in which you will have to interpret physical data. No detailed derivation will be required (e.g. of the solution to the Schrödinger equation of the hydrogen atom), but you should know the starting point (e.g. Schrödinger equation), ansatz (e.g. separation of wave function into a radial and an angular part), and principal solution (e.g. that the solution to the angular Schrödinger equation of the hydrogen atom are the spherical harmonics and that the hydrogen energy is -13.6 eV / n2).

### Suitable literature

• W. Demtröder, Atoms, Molecules and Photons, Springer, 2006, available as e-book from the University Library
• S. Andersson, F. Bruhn, J. Hedman, L. Karlsson, S. Lunell, K. Nilson, & J. Wall, Atom- och molekylfysik, Uppsala universitet
• H. Haken & H. C. Wolf, The Physics of Atoms and Quanta, Springer, 2005 (or earlier editions), available as e-book from the University Library
• A. Thorne, U. Litzén, & S. Johansson, Spectrophysics

### Practice questions

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