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The great Soviet physicist Lev Landau developed a famous entry exam to test his students. This "Theoretical Minimum" contained everything of what he considered elementary for a young theoretical physicist. Despite its name, it was and still is, extremely rigorous and comprehensive.
Nowadays students are examined by collaborators of Landau Institute for Theoretical Physics. Each exam, as it was before, consists of problems solving. For every exam there is one or several examiners with whom the potential candidate is to establish contact in order to make an appointment for particular exam. Normally the student wishing to attempt the examination is expected to do so at Landau Institute for Theoretical Physics at Moscow, but it is not feasible for overseas candidates. Therefore, in such cases the examiner would send the candidate problems via email and the detailed solutions should be sent back in 3-7 days. The solutions are to be submitted in LaTeX PDF format.
The syllabus for each exam corresponds to the contents of volumes in the Course of Theoretical Physics by Lev Landau & Evgeny Lifshitz. Usually one is expected to master every paragraph of the book, literally! Here is the detailed syllabus :
- Mathematics-I : Three Problems in indefinite Integration, differential equations and limits, vector algebra and tensor analysis.
- Mechanics : Volume 1. Theoretical mechanics, except section § 27, 29, 30, 37, 51
- Field Theory : Volume 2. The Classical Theory of Fields, except section § 50, 54-57, 59-61, 68, 70, 74, 77, 97, 98, 102, 106, 108, 109, 115-119
- Mathematics-II : Theory of functions of a complex variable, evaluating integrals, solution of equations deductions using contour integrals (Laplace's method), calculate asymptotics of integrals, special functions (Bessel, Legendre, elliptic, the hypergeometric function, the gamma function).
- Quantum Mechanics : Volume 3. Quantum Mechanics : Non-Relativistic Theory, except sections § 29, 49, 51, 57, 77, 80, 84, 85, 87, 88, 90, 101, 104, 105, 106, 110, 114, 138, 152.
- Quantum Electrodynamics : Volume 4. Quantum Electrodynamics, except section § 9, 14, 16, 31, 35, 38, 41, 46, 48, 51, 52, 55, 57, 66, 70, 82, 84, 85, 87, 89, 91, 95, 97, 100, 101, 106, 109, 112, 115-144
- Statistical Physics-I : Volume 5. Statistical Physics Part I, except sections § 22, 30, 50, 60, 68, 70, 72, 79, 80, 84, 95, 99, 100, 125-127, 134-141, 150-153, 155-160
- Continuum mechanics : Volume 6. Fluid Mechanics, except sections § 11, 13, 14, 21, 23, 25, 28, 30-32, 34-48, 53-59, 63, 67-78, 80, 83, 86, 88, 90, 91, 94-141; Volume 7. Theory of Elasticity, except sections § 11, 13, 14, 21, 23, 25, 28, 30-32, 34-48, 53-59, 63, 67-78, 80, 83, 86, 88, 90, 91, 94-141
- Electrodynamics of continuous media : Volume 8. Electrodynamics of continrous media, except § 1 to 5, 9, 15, 16, 18, 25, 28, 34, 35, 42, 44, 56, 57, 61, 64, 69, 74, 79-81, 84, 91-112, 123, 126.
- Statistical Physics-II : Volume 9. Statistical Physics Part II, only § 1-5, 7, 18, 22, 27, 29, 36, 40, 43, 48, 50, 55, 61, 63, 65, 69
- Physical Kinetics : Volume 10. Physical Kinetics, only § 1 to 8, 11, 12, 14, 21, 22, 24, 27, 30, 32-34, 41-44, 66-69, 75, 78, 82, 86, 101.
As a side note, the exam Quantum Mechanics also serves as graduate entrance exam for the institute. I will be posting my notes and those which will be helpful for those who wish to attempt it soon.