In recent years Leonard Susskind has been giving an excellent series of lectures on basic ideas of theoretical physics, under the title The Theoretical Minimum. The general idea seems to be to provide something in between the usual sort of popular book about physics (which avoids equations and tries to give “intutitive” explanations in ordinary language) and conventional undergraduate-level textbooks. Such textbooks generally assume college-level multi-variable calculus, differential equations and linear algebra, and often skip lots of detail and motivation, assuming that the book is a supplement to a standard course of lectures.

For Susskind’s lectures, you mostly just need high-school level mathematics, up to some some basic differential calculus, as well as two by two matrices. Actually though, if you’ve never seen matrices and very simple linear algebra, this is a good place to learn some basics examples of this subject.

A year ago the first book version of some of the lectures appeared as The Theoretical Minimum, with George Hrabovsky writing up Susskind’s lectures on classical mechanics. I wrote a little bit about the book here, and was quite impressed by the way it managed to give the details of the formalism of Hamiltonian mechanics, while sticking to as simple and concrete mathematics and calculational tools as possible.

Today is publication day for the next volume, Quantum Mechanics: The Theoretical Minimum, which is a joint effort this time with Art Friedman. It’s even better than the first volume, taking on a much more difficult subject. About the first two-thirds of the book sticks to the simplest possible quantum system, one with a two-dimensional state space. The linear algebra needed is developed from scratch and Susskind works out at a very leisurely pace all the details of what the quantum picture of reality looks like in this simplest context. There’s a lot about what “entanglement” really is, and this part ends up with an introduction to Bell’s theorem.

The last third of the book is a quicker-paced trip through the usual material about wave-functions and the Schrödinger equation, ending up with the details for the harmonic oscillator potential.

“The Theoretical Minimum” phrase is a reference to Landau, but it’s a good characterization of this book and the lectures in general. Susskind does a good job of boiling these subjects down to their core ideas and examples, and giving a careful exposition of these in as simple terms as possible. If you’ve gotten a taste for physics from popular books, this is a great place to start learning what the subject is really about.

I only noticed one mistake in the book, on its back cover, where one of the blurbs is attributed to a Professor of Mathematics at Columbia, when I know for a fact that his actual title there is “Senior Lecturer”. Susskind does have a bit of history of getting this point wrong, but probably the fault here lies with the publisher.

**Update**: Nature has a review here.

I just finished reading the Theoretical Minimum. Thank you for mentioning it in your blog or I would not have thought to read it. I particularly like the way that the book re-derived calculus and showed how the Fundamental Theorem of the Calculus could be used in physics to solve some kinds of problems.

My degree was in Electrical Engineering in 1980, so I had taken most of the background science classes that Susskind is describing. However, I do not recall the concept of the Lagrangian being discussed in my physics or electrical engineering classes. It was at this point in the book, that I wish the author had gone into a little more detail about how Action differs from Work or at least more into the thinking process that led to Lagrange’s equation. The difference between kinetic and potential energy, as I recalled, was the work. Sadly this disconnect between my recollection of my physics classes and the introduction of this new material left me a bit confused through the remainder of the book. I am however, hungry to understand Lagrangian and Hamiltonian mechanics better. Is there a another book on the subject that you might recommend?

Thanks,

Lowell Boggs

Lowell Bogg,

Sorry but this isn’t material I’ve taught at this level, and I don’t know the textbooks. When I studied the subject at an advanced undergraduate level the textbook was Goldstein’s Classical Mechanics, but I found that rather dry and hard going. Presumably there are some good modern textbooks, at a bit lower level than Goldstein, maybe others can suggest a good one.

The classical dynamics text I used as an undergraduate was Thornton & Marion, Classical Dynamics of Particles and Systems, which has a chapter devoted to the Lagrangian and Hamiltonian. I don’t know if anything new has come up in the decade plus since I took that class as a sophomore physics student, though. Looking at the textbook now, the introduction to the chapter seems pretty good; it does the thing I very much appreciate in physics textbooks of explaining

whyyou would want to do something a particular way, not justhowto do it that way.The review of classical mechanics in chapter 2 of Shankar’s quantum mechanics textbook* is quite good. It’s very brief, as it starts with the principle of least action and goes through the Lagrangian and Hamiltonian formulations of mechanics in about 30 pages. Obviously, a lot is left out, but for a quick and intuitive introduction to the ideas at the undergraduate level, I found it was pretty nice.

*R. Shankar,

Principles of Quantum MechanicsI haven’t read Susskind’s TM books, but I have the feeling that the theoretical Universe has rolled off to decay into a considerably lower TM since L & L.

I haven’t read Susskind’s TM books, but I have the feeling that the theoretical Universe has rolled off to decay into a considerably lower TM since L & L.According to wikipedia, only 43 people passed the famous “theoretical minimum” exam between 1934 and 1961.

Lowell Bogg:

when I looked up Susskind’s book by following the link Peter gives above, Amazon.com in its wisdom guided me to “A Student’s Guide to Lagrangians and Hamiltonians” by Patrick Hamill. From the reviews, it seems to be quite good.

Taylor’s “Classical Mechanics” is as good as they come.

Thanks, I didn’t know about the books. I went from freshman physics to the theoretical minimum by watching Susskind’s lectures on classical mechanics and QM on youtube, and I can veryify from that perspective that they are excellent. I’m looking forward to the rest of his lectures and to reading the books.

Senior lecturers in math at Columbia have done some excellent work, though I didn’t know that Susskind was so happy with their reviews of his work.

“… reference to Landau …”

https://en.wikipedia.org/wiki/Kharkiv_Theoretical_Physics_School

Visually, this new book is a stinker; production values are noticeably worse than in the classical dynamics volume. I’d soon be exhausted trying to work through it.

That aspect aside, I’d love to hear why one would be better served with this book than with volume 3 of the Feynman lectures (available free on-line). (By the way, Vol II ch. 19 includes a v nice introduction to the Lagrangian approach.)

I recall in ~ 1974 Wendell Furry teaching EMT based on Landau and Lifshitz’s “Electodynamics of Continuous Media”. It certainly was an eye opener for a young guy “raised” on Jackson. Not sure what I feel about physics students lectured from either the “dumbed down” or “scaring off” sources.

I may just give these a look. I recently took an intermediate stats class and a course in electrophysiology, and was happy to see that my math muscles, such as they are, haven’t completely atrophied. I’ve done the calc and actually had some linear algebra in a pre-calc course (unorthodox high-school math teacher), but it’s been ages. I don’t know why, because I’ll probably never use it professionally, but somehow dabbling in such things on the side does me a lot of good.

I personally don’t think there is a textbook that competes with Goldstein’s Classical Mechanics or with Jackson’s Classical Electrodynamics. Probably no one thinks their time is worth the effort to come up with a better textbook.

Fetter and Walecka is a better is better than Goldstein

As a textbook Gregory´s Classical Mechanics chapters on actions, lagrangians and hamiltonians are both short and very clear, with plenty of good examples and exercises.

Taylor´s and Kibble´s book are pretty good too.

Perhaps surprisingly, the first chapters of A. Zee Eintein´s Gravity in a Nutshell contain an amusing introduction to variational calculus, actions and lagrangians.

For the historical and metaphysical context of the action principle and its origins, Ivar Ekeland book The best of all possible worlds gives an excellent, and very readable and insightful introduction

Many thanks to all who suggested ideas for further reading. I have ordered the Hamill book and have read through the Feynman lecture on the principle of least action. And “work” has nothing to do with it.

Thanks Again!

Lowell

Maybe that’s enough comments about people’s feelings concerning which textbooks on a completely different topic at a completely different level they like or don’t like…

Be aware that there are older versions of Susskind’s lectures at http://www.newpackettech.com/Resources/Susskind/PHY25/QuantumMechanics_Overview.htm The newer lectures are at http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter

I made the mistake of watching the older ones which aren’t as closely coordinated with the book that I am over halfway through.

At my age, I find the book challenging and the logic sometimes discontinuous. (Not trying to pun.) Perhaps I should have just watched the lectures.

Consider this book Cornelius Lanczos – “Variational principles in Mechanics”