
Atom och molekylfysik FYSC11  HT 2013
Course information and updated scheduleCourse information and updated schedule (29 August 2013)
Compulsory handin exercises
Exams from earlier semesters
Planning and reading suggestionsList of subjects and reading suggestions
CompendiumCompendium, covering QM intro and hydrogen atom
Compulsory reading, exercises for following lecture, material from lectures
Monday, 2 SeptemberBrief presentation of the history of atomic physics & some examples from modern atomic physicsReading for tomorrow: compendium pp. 115 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 SeptemberPowerpoint material from the lectureReading for tomorrow: compendium pp. 1530 Exercise for tomorrow: Express the S_{x}> vector in terms of the S_{y}> vectors. Apply the S_{z} operator to the S_{x}> vectors. Wednesday, 4 SeptemberReading for tomorrow: compendium pp. 3042Exercise for tomorrow: Write down the matrix expression for the S_{z} operator in the {S_{z},+>,S_{z},>}, {S_{x},+>,S_{x},>}, and {S_{y},+>,S_{y},>} bases. Thursday, 5 SeptemberReading for Tuesday, 10 September: compendium pp. 4262Exercise for Tuesday, 10 September:
Tuesday, 10 SeptemberReading for tomorrow: compendium pp. 6272Exercise for tomorrow: Show that T(dx') = 1i K dx', with K=(K_{x}, K_{y}, K_{z}) a tuple of Hermitian operators, fulfills the following requirements:
Wednesday, 11 SeptemberExercise for tomorrow:Solve the three first tasks after equation (4.28) in the compendium. Thursday, 12 SeptemberExercise for tomorrow: Solve the remaining tasks on pp. 60 and 61 in the compendium.Friday, 13 SeptemberReading 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 SeptemberReading for tomorrow: Demtröder section 5.8.Exercise for tomorrow: Show for the l, s, and j quantum numbers that j ≤ l+s and ls ≤ j, and thus ls ≤ j ≤ l+s. Tuesday, 17 SeptemberPowerpoint material from the lectureExercise for tomorrow: calculate the transition matrix element for an optical transition between the hydrogen 1s and 2p states for light with polarisation along the zaxis. Choose the same m_{l} and m_{s} for the initial and final state. Wednesday, 18 SeptemberReading for tomorrow: Helium atom (e.g. Demtröder 6.1).Thursday, 19 SeptemberReading 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 H_{α} 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 SeptemberWe started dealing with the helium atom.No reading, no exercise. Monday, 23 SeptemberWe went on with treating the helium atom and started on multielectron atoms: hamiltonian, central field approximation, aufbau principle.Powerpoint material from the lecture Monday, 14 OctoberAfter some recapitulation of the helium atom (Coulomb and exchange integrals, ) we had a look at the SCF and HartreeFock 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 OctoberWe discussed the noncentral part of the potential and compared it in size to the spinorbit 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 LSterms for a p^{2} configuration.Reading for tomorrow: Vibrations and rotations in molecules (e.g. Demtröder 6.5) Exercise: Write down the possible terms for a p^{3} configuration. Wednesday, 16 OctoberWe discussed vibrations in molecules in the harmonic approximation. Then we considered vibrational transitions in infrared absorption and emission and the Raman effect.Thursday, 17 OctoberWe 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, D_{e}, and α for the A ^{2}Π state of carbon monoxide. Thursday, 17 OctoberWe 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, D_{e}, and α for the A ^{2}Π state of carbon monoxide.
ExamThe written exam will take place on Friday, 25 October. As a preparation for the exam, you should look at the following things:
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 handin 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 / n^{2}).
Suitable literature
Practice questions
Practice questions for the exam
