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Most students meet physics one chapter at a time, and few ever ask which methods they must own before they can call a subject theirs. Lev Landau answered that question with a list of exams. This post covers what Landau did, verified from Nobel Prize records, what his "theoretical minimum" looks like today, a worked example of the scaling reasoning theorists use, and a routine you can borrow.
Who was Lev Landau?
Landau was born in Baku on 22 January 1908. The presentation speech at his Nobel ceremony notes that he began his studies at the University of Leningrad at 14. His Nobel biography records that he graduated from its physics department at 19, then spent 1929 to 1931 abroad, partly as a Rockefeller Foundation Fellow, working in Germany, Switzerland, England and above all in Copenhagen under Niels Bohr. You can read about Bohr's own approach in our post on Niels Bohr and his model of the atom.
From 1932 to 1937 he led the theoretical department of the Ukrainian Physico-Technical Institute at Kharkov. From 1937 he headed the theoretical department of the Institute for Physical Problems in Moscow. The biography says his work covered "all branches of theoretical physics, ranging from fluid mechanics to quantum field theory".
What did Landau win the Nobel Prize for?
The 1962 Nobel Prize in Physics went to Landau alone, "for his pioneering theories for condensed matter, especially liquid helium". Pyotr Kapitsa had discovered in 1938 that liquid helium becomes superfluid, flowing without friction a couple of degrees above absolute zero. In 1941 Landau applied quantum theory to this motion and introduced quasiparticles as the equivalent of sound vibrations and vortices, which let him explain superfluidity. Our post on Pyotr Kapitsa and superfluidity covers the experiment side of the story.
Landau could not travel to Stockholm. The presentation speech explains that he had not fully recovered from a severe accident at the start of 1962, so the prize was handed to him in Moscow by the Swedish ambassador. He died on 1 April 1968.
What is the theoretical minimum?
In 1962 Landau and E.M. Lifshitz also received the Lenin Prize for their Course of Theoretical Physics, according to the Nobel biography. That course is the backbone of what is still called Landau's theoretical minimum, a set of exams now run through the Landau Institute for Theoretical Physics.
The official site describes it this way:
There are 11 exams in the main branches of mathematics and theoretical physics: Mathematics I, Mechanics, Field Theory, Mathematics II, Quantum Mechanics, Quantum Electrodynamics, Statistical Physics I, Mechanics of Continuous Media, Electrodynamics of Continuous Media, Statistical Physics II and Physical Kinetics.
Anyone who wishes may take them, in any order.
Each exam is arranged one to one with a named examiner.
The physics exams follow the Landau and Lifshitz course. The Mechanics exam, for example, covers all of Volume 1 except five listed sections.
The site keeps a public list of everyone who has passed each exam, and it was still adding names in 2026.
Worked example: Kepler's third law from scaling alone
Theorists often learn a lot from how an equation scales before solving it. Here is a short argument of that kind, using only Newton's second law.
Suppose a particle moves in a potential U that is proportional to r^k. Stretch every length by a factor α and every time by a factor β. Ask when the stretched motion is still a solution.
The left side, m d²r/dt², scales as α/β², because the length goes up by α and time squared by β².
The force is −dU/dr, which is proportional to r^(k−1), so it scales as α^(k−1).
Setting them equal gives α/β² = α^(k−1), so β² = α^(2−k) and β = α^(1 − k/2).
Now try three cases:
Gravity, k = −1. β = α^(3/2), so T² is proportional to a³. That is Kepler's third law. An orbit 4 times larger has a period 4^(3/2) = 8 times longer.
Spring, k = 2. β = α^0 = 1. The period does not depend on amplitude, which is the defining feature of simple harmonic motion.
Uniform gravity near the ground, k = 1. β = α^(1/2). Quadruple the height and the fall time doubles, which matches t = √(2h/g).
Two mistakes to watch for. First, students scale lengths but forget that time must scale too; the whole point is to find β. Second, they mix up the power in the potential and the power in the force. A force proportional to 1/r² comes from a potential proportional to 1/r, so k = −1, not −2. Our post on Kepler's laws of planetary motion shows the observations this one line explains.
What can a student take from Landau's way of working?
The theoretical minimum makes three habits concrete. It defines the core in advance, so there is no doubt about what counts. It tests that core one piece at a time, with another person checking you. And it ties each exam to one well-defined text rather than a pile of books.
You can build the same structure for your own syllabus:
Write your minimum. For one subject, such as mechanics, list eight to ten methods you must use without notes: free-body diagrams, energy conservation, momentum in collisions, rotational dynamics, and so on.
Choose one main text per method. Use your NCERT chapter or one standard book, not five.
Get examined. Ask a friend or teacher to set you two problems on one item, and solve them out loud. Pass or fail, write it down.
Keep a pass list. Like the public list on the theoretical minimum site, track which items you have passed and when. Retest each one after a few weeks.
When a test exposes a gap in one method, fix that gap before moving on. The Fermi Concept Library has every concept in physics and mathematics with its own lesson, so you can relearn a single idea and return to your list.
This week, write your own ten-item minimum for mechanics and get examined on the first item.
