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On Solutions to the Theoretical Minimum (Classical/Quantum Mechanics)

date: 2022-09-08
update: 2024-04-15

The Theoretical Minimum is a book series by Leonard Susskind, and others, containing three books, with a fourth one to be published soon:

  1. Classical Mechanics, with George Hrabovsky;
  2. Quantum Mechanics, with Art Friedman;
  3. Special Relativity and Classical Field Theory, with Art Friedman again;
  4. General Relativity, with André Cabannes, who contributed to the French translation of the three previous works.

The books are relatively short (say, compared to Feynman’s lectures), self-contained (well, depending on how curious you are; they do go as far as to cover a great deal of mathematical background, but they just can’t be exhaustive either), and, at least for the Classical Mechanics one, aimed at presenting general theoretical formulations: the Lagrangian and Hamiltonian formalisms, based on the stationary-action principle and the principle of conservation of energy.

They all come with a few exercises, often rather simple, focused on making sure you understand the key concepts.

Einstein, sanguine on paper

Einstein, sanguine on paper by M. Bivert through instagram.com

Solutions

Note: The first two volumes are essentially complete. Two exercises (cm/L06E05, cm/L07E05) should be missing for the first volume, as I’d like to push them a little further than what the authors intended to.

Classical mechanics Quantum mechanics Special relativity
and Classical Field Theory
L01E01.pdf (.tex);
L01E02.pdf (.tex);
L01E03.pdf (.tex);
I01E01.pdf (.tex);
I01E02.pdf (.tex);
I01E03.pdf (.tex);
I01E04.pdf (.tex);
I01E05.pdf (.tex);
I01E06.pdf (.tex);
L02E01.pdf (.tex);
L02E02.pdf (.tex);
L02E03.pdf (.tex);
L02E04.pdf (.tex);
L02E05.pdf (.tex);
L02E06.pdf (.tex);
L02E07.pdf (.tex);
L02E08.pdf (.tex);
I02E01.pdf (.tex);
I02E02.pdf (.tex);
I02E03.pdf (.tex);
I02E04.pdf (.tex);
L03E01.pdf (.tex);
L03E02.pdf (.tex);
L03E03.pdf (.tex);
L03E04.pdf (.tex) (.html);
I03E01.pdf (.tex);
I03E02.pdf (.tex);
L05E01.pdf (.tex);
L05E02.pdf (.tex);
L05E03.pdf (.tex);
L06E01.pdf (.tex);
L06E02.pdf (.tex);
L06E03.pdf (.tex);
L06E04.pdf (.tex);
L06E06.pdf (.tex);
L07E01.pdf (.tex);
L07E02.pdf (.tex);
L07E03.pdf (.tex);
L07E04.pdf (.tex);
L08E01.pdf (.tex);
L08E02.pdf (.tex);
L10E01.pdf (.tex);
L10E02.pdf (.tex);
L10E03.pdf (.tex);
L11E01.pdf (.tex);
L11E02.pdf (.tex);
L11E03.pdf (.tex);
L11E04.pdf (.tex);
L11E05.pdf (.tex);
solutions.pdf (.tex) 		L01E01.pdf (.tex);
L01E02.pdf (.tex);
L02E01.pdf (.tex);
L02E02.pdf (.tex);
L02E03.pdf (.tex);
L03E01.pdf (.tex) (.html);
L03E02.pdf (.tex);
L03E03.pdf (.tex);
L03E04.pdf (.tex);
L03E05.pdf (.tex);
L04E01.pdf (.tex);
L04E02.pdf (.tex);
L04E03.pdf (.tex);
L04E04.pdf (.tex);
L04E05.pdf (.tex);
L04E06.pdf (.tex);
L05E01.pdf (.tex);
L05E02.pdf (.tex);
L06E01.pdf (.tex);
L06E02.pdf (.tex);
L06E03.pdf (.tex);
L06E04.pdf (.tex);
L06E05.pdf (.tex);
L06E06.pdf (.tex);
L06E07.pdf (.tex);
L06E08.pdf (.tex);
L06E09.pdf (.tex);
L06E10.pdf (.tex);
L07E01.pdf (.tex);
L07E02.pdf (.tex);
L07E03.pdf (.tex);
L07E04.pdf (.tex);
L07E05.pdf (.tex);
L07E06.pdf (.tex);
L07E07.pdf (.tex);
L07E08.pdf (.tex);
L07E09.pdf (.tex);
L07E10.pdf (.tex);
L07E11.pdf (.tex);
L07E12.pdf (.tex);
L08E01.pdf (.tex);
L09E01.pdf (.tex);
L09E02.pdf (.tex);
L09E03.pdf (.tex);
L10E01.pdf (.tex);
solutions.pdf (.tex) 		L01E00.pdf (.tex);
solutions.pdf (.tex)

Note: The solutions.pdf files contain the all available solutions for each book (concatenating of all the [LI]xxEyy.pdf essentially).

Note: The .tex and .pdf are all available on Github.

Note: cm/L03E04 is the first exercise in the book introducing the reader to the (classical) harmonic oscillator. Given its theoretical importance, I’ve went more in-depth that what was asked; the “solution” is also available as an html page. Similarly, qm/L03E01 contains an detailed proof of (most of) the (real) spectral theorem, a fundamental mathematical result in quantum mechanics, especially in its generalized form to infinite-dimensional Hilbert spaces, and is also available in a dedicated html page

Other solutions

I’ve been collecting/using a few other sources of solutions. The approaches sometimes and different, and I haven’t but on a few peculiar occasions made a direct comparison, so you might want to check those:

Note: Use Google translate for non-English ressources.

Intuitive mathematics

A “downside” of physics textbooks is often that some proofs/notations lack clarity and/or mathematical rigor (but not necessarily correctness!): physicists are known to be rather peculiar mathematicians [Redish2006].

When studying physics, this can be important to keep this in mind; physicists are bright people, they move fast: having a solid mathematical anchor can definitely help to follow them. On the other hand, physicists’ intuition can also help shine some lights on obscure mathematical constructions.

Note: Physicists use mathematics in a more intuitive/spontaneous way, by comparison to the painstakingly meticulous approach of pure mathematicians. Interestingly, we can link that dichotomy to the distinction in Chinese painting between Gongbi (工筆) and Shuimo (水墨):

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Shrike in a barren tree, 枯木鳴鵙図, Koboku meigeki-zu

Shrike in a barren tree, 枯木鳴鵙図, Koboku meigeki-zu by Miyamoto Musashi (宮本 武蔵, c. 1584 – 13 June 1645) through wikimedia.com – Public domain

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Additional resources

If you’re here, it’s likely that you intend to study physics to some degree: the following resources could then be of interest, although they tend to go far beyond what is strictly necessary to study from Susskind’s books, which again, are for the most part self-contained.

In no order of preference:

Portrait of Émilie du Châtelet (1706-1749), huile sur toile, 18th century, 120×100 cm (47.2×29.3 in)

Portrait of Émilie du Châtelet (1706-1749), huile sur toile, 18th century, 120×100 cm (47.2×29.3 in) by Maurice Quentin de La Tour (1704 – 1788) through wikimedia.org – Public domain

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