6 EC
Semester 1, period 2
5092ATPH6Y
Atoms are the building blocks of the world around us. As all atoms of a given species are identical and have a relatively simple structure they are particularly suited for precision tests of theoretical models and for the application in precision measurements. This has resulted in seminal discoveries and is the starting point for the understanding of chemistry and condensed matter physics.
We start with a review of quantum mechanical motion in a central potential field. After obtaining the rotational quantum numbers and the radial wave equation for a single electron we obtain the famous Bohr formula for the energy levels. We calculate radial averages and electric-dipole transition matrix elements. Atomic fine structure: we calculate relativistic level shifts and generalize the electronic momentum to describe motion in a magnetic field and the orbital Zeeman coupling. Introducing spin we find the spin Zeeman Effect and spin-orbit coupling. For hydrogen-like many-electron atoms the fine structure is dominated by screening of the nuclear charge by the electron cloud. Hyperfine structure: we discuss the nuclear Zeeman coupling as wel as the hyperfine coupling between the nuclear spin and the electronic angular momentum.
The discussion of many-electron atoms starts with helium. We show that screening results in an effective potential for the electronic motion which is used to calculate the helium ground state. We meet the evidence for exchange degeneracy and Pauli Exclusion Principle. We introduce Slater integrals to calculate the Coulomb repulsion between the electrons. Turning to atoms with more than two electrons we introduce the central field approximation. We introduce many-electron wavefunctions in the form of Slater determinants of spin orbitals. We evaluate matrix elements between Slater determinants and derive the Hartree-Fock equations for the orbitals. We obtain electron configurations and the shell model for the atomic structure.
This is a course with 14 formal lectures in which the basic principles of atomic physics are outlined.
Lots of material can be found in the written Lecture Notes.
The course builds heavily on the mathematics and physics skills acquired in the first two years of the physics study. To create awareness of this feature, the recommended prior knowledge is summarized in Appendices and referenced in the main text.
The mandatory knowledge for the exam is indicated in a detailed reader.
Every subject is trained in exercise classes, which prepare the student for two mandatory partial exams.
Importantly: The student is free to go into any depth. Since students with strongly varying interests and skills are participating in the course, personalized feedback is given in the exercise classes.
Activiteit | Uren | |
Deeltoets | 3 | |
Hoorcollege | 30 | |
Tentamen | 3 | |
Vragenuur | 2 | |
Werkcollege | 30 | |
Zelfstudie | 100 | |
Totaal | 168 | (6 EC x 28 uur) |
Programme's requirements concerning attendance (TER-B):
| Item and weight | Details |
|
Final grade | |
|
1 (100%) Deeltoets |
Contact the course coordinator to make an appointment for inspection.
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl
| College nr | Onderwerpen | Studiestof |
| 1 | Motion in central potential field | Chapter 1 |
| 2 | Hydrogenic atoms | Chapter 2 |
| 3 | Angular momentum | Chapter 3 |
| 4 | Fine structure I | Chapter 4 |
| 5 | Fine structure II | Chapter 4 |
| 6 | Hyperfine structure | Chapter 5 |
| 7 | Hyperfine structure | Chapter 5 |
| 8 | Helium-like atoms | Chapter 7 |
| 9 | Many-electron atoms | Chapter 8 |
| 10 | Many-body wavefunctions | Chapter 9 |
| 11 | Aufbau principle | Chapter 10 |
| 12 | Justification of Hunds rule I & II | Chapter 10 |
| 13 | Justification of Hunds rule III | Chaper 10 |
Recommended prior knowledge: Lagrangian and Hamiltonian formalism from classical mechanics; the concept of scalar and vector potentials from classical electrodynamics; the principles of quantum mechanics, in particular quantized angular momentum, linear algebra of Hilbert spaces as used in the Dirac formalism and the elements of perturbation theory.