Atomic Physics

Course manual 2021/2022

Course content

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.

Study materials

Syllabus

• Atomic Physics

Objectives

• explain the theory of atomic structure for most atoms of the periodic system
• apply quantum mechanics to atomic systems, in particular the rules of angular momentum and time-independent perturbation theory
• point to the experimental evidence for seminal discoveries in atomic physics
• explain the Aufbau principle for the periodic system as well as the origin of the Hund rules for the atomic ground state
• determine the electronic ground state and analyze the magnetic properties of most atoms of the periodic system

Teaching methods

• Lecture
• Self-study
• Supervision/feedback meeting

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.

Learning activities

Attendance

Programme's requirements concerning attendance (TER-B):

• Each student is expected to participate actively in each component of the programme that he/she signed up for. A student that does not attend the first two seminars of a course, will be administratively removed from the seminar group. A request for reregistration for the seminars can be applied to the programme coordinator.
• If a student cannot attend an obligatory component of a programme's component due to circumstances beyond his control, he must report in writing to the relevant teacher as soon as possible. The teacher, if necessary after consulting the study adviser, may decide to issue the student a replacing assignment.
• It is not allowed to miss obligatory commponents of the programme if there is no case of circumstances beyond one's control.
• In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are set down in advance in the course manual.
• In addition to the above mentioned rules, in the first semester of the first year a student should be present in at least 80% of the seminars. Moreover, participation to midterm tests and obligatory homework is required. If the student does not comply with these obligations, the student is expelled from the resit of this course. Students in the double Bachelor's degree programme Mathematics and Physics are exempted from this requirement. In case of personal circumstances, as described in OER-A Article A-6.4, a different study plan will be made in consultation with the study advisor.

Assessment

Inspection of assessed work

Contact the course coordinator to make an appointment for inspection.

Fraud and plagiarism

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

Course structure

Timetable

The schedule for this course is published on DataNose.

Additional information

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.

Processed course evaluations

Enhanced credit for understanding over credit for reproduction

Contact information

Coordinator

• dr. R. Gerritsma

Staff

• dr. R. Gerritsma
• Prof. Jook Walraven
• Eleanor Trimby MSc
• Andrés Martínez de Velasco MSc