FSI3005 Qualitative and Approximate Methods in Theoretical Physics 5.0 credits

The course is devoted to some "tools of the trade" in theoretical physics, the methods that are widely used by experienced theorists but rarely taught in a single course. These are the qualitative and approximate methods that allow one to reveal the characteristic features of the studied problem and in many cases find its approximate solution without (or prior to) finding the full solution of the problem.

Normally, the knowledge of these methods comes with experience and is a part of the "folklore" of theoretical physics. The present course is an attempt of collecting some of these approaches in a single course.

The topics to be covered include: Estimates of mathematical expressions (derivatives and integrals), approximate methods of solving algebraic and differential equations, dimensional analysis, model estimates in physical problems (including problems in quantum mechanics and atomic physics), various cases of perturbation theory, sudden and adiabatic perturbations, WKB approximation, methods based on analytic properties of physical quantities, qualitative methods in relativistic quantum mechanics, quantum field theory and particle physics (no prior knowledge of which is assumed).

After completed course, the PhD student should be able to:

• know some "tools of the trade" in theoretical physics.
• estimate mathematical expressions.
• use dimensional analysis.
• perform model estimates in physical problems.
• use various methods of perturbation theory.
• use qualitative and approximate methods.

The course will be of interest to PhD students who specialize or want to specialize in theoretical physics, as well as to young researchers working in this field.

Elementary calculus, elementary complex analysis, classical mechanics and electrodynamics, quantum mechanics.

• A.B. Migdal, Qualitative methods in quantum theory, W.A. Benjamin, Reading, Advanced Book Program, 1977. (Frontiers in physics, v. 48)
• L.I. Sedov, Similarity and dimensional methods in mechanics, CRC Press, Boca Raton, 1993.
• A. Erdelyi, Asymptotic expansions, Dover, New York, 1956.

If the course is discontinued, students may request to be examined during the following two academic years.

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Hand in assignments and an oral exam.

Tommy Ohlsson

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.