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Quantum Mechanics: The Theoretical Minimum

(Theoretical Minimum)

Leonard Susskind,

Art Friedman

4.34 · Rating details · 1,173 ratings · 110 reviews

From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum physics

First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics.

In this follow-up to The Theoretical Minimum, Su ...more

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Hardcover, 364 pages

Published February 25th 2014 by Basic Books (first published January 1st 2014)

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Sep 11, 2014 Manny rated it it was amazing · review of another edition

Recommended to Manny by: Anyone who wants to understand quantum mechanics and knows some math

Shelves: science

I've finished volume one and now I'm dying to find out what happens next. Talk about a cliffhanger ending!
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I must confess that I didn't enjoy the second volume quite as much as the first, but that mainly shows how high the bar was; this is still the best introduction to quantum mechanics I have ever seen, and if you have some mathematical background (linear algebra, calculus) I can't recommend it too highly. It requires some effort to read, but it's definitely wo I've finished volume one and now I'm dying to find out what happens next. Talk about a cliffhanger ending!
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I must confess that I didn't enjoy the second volume quite as much as the first, but that mainly shows how high the bar was; this is still the best introduction to quantum mechanics I have ever seen, and if you have some mathematical background (linear algebra, calculus) I can't recommend it too highly. It requires some effort to read, but it's definitely worth it.

The overall plan is extremely well thought out. Most books on quantum mechanics start off by introducing the quantum versions of position and momentum, so that they can get to Heisenberg's Uncertainty Principle as quickly as possible. After reading Susskind and Friedman, I am sure this is a mistake. The problem is that we know what position and momentum mean in classical physics, so it's impossible to read about their quantum analogs without thinking that they're basically the same thing. They aren't: quantum mechanics is much weirder and much more interesting, but you don't immediately notice.

Instead of taking this tired old road, Susskind chooses a completely different starting-point, the concept of spin. Spin is a truly quantum mechanical concept, which is so different from classical angular momentum that there is no possibility of confusing them. If you've read any quantum mechanics at all, you'll know that spin can be either "up" or "down". But how can this make sense, when you stop and think about it? Surely we need three independent directions, corresponding to the x, y and z axes, rather than two directions which, to make things even more counter-intuitive, are oriented along the same axis?

But it does make sense. We start by considering a device that measures an electron's spin. We orient it vertically, and it only ever gives two possible readings: +1, or "up", and -1, or "down". Now we rotate it 90 degrees, so that the two readings instead mean "left" and "right". If the electron was previously in the "up" state, a naive guess might be that we'll now get a zero reading. Wrong! There is no zero reading; we'll get "left" or "right" with equal probability; so "up" must be a combination of "left" and "right", where the two components are in some sense given equal weight. Similarly, when we orient the apparatus along the third axis, we find that "left" and "right" are combinations of "in" and "out". In fact, each of the "up"/"down", "left"/"right" and "in"/"out" pairs can be expressed in terms of any of the others, and there is a simple mathematical way to write down the relationships using matrix algebra and complex numbers. It all works, and you can see why!

I was hooked. Forget that stupid cat, which only appears here as the subject of a couple of ironic jokes. This is the right way to do it.
...more

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Nov 25, 2018 Manuel Antão rated it really liked it · review of another edition

Shelves: 2018

If you're into stuff like this, you can read the full review.

ΔE Δt ≥ ℏ/2: "Quantum Mechanics: The Theoretical Minimum" by Leonard Susskind, Art Friedman

I was on a train the other week and I was sitting opposite Einstein who asked me if I would mind changing seats because he liked to see where he was going for a half a journey and then he liked to see where he had been for the other half of the journey and I told him I didn't mind changing seats and I asked him if he minded me asking him if he wa ...more

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Mar 01, 2014 WarpDrive rated it it was amazing

Shelves: science-and-maths

This is a really nice introductory book on Quantum Mechanics - Quantum Mechanics done for real, with some decent detail and good mathematical treatment of some of its most important aspects.

As a list of prerequisites for fully enjoying this book, I would recommend the following:
- read volume 1 (on Classical Mechanics) which is simply fantastic on its own
- basic knowledge of linear algebra, calculus and complex vector (Hilbert) spaces

The author is great at explaining potentially tricky and compl ...more

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Oct 12, 2020 Bernardo rated it it was amazing · review of another edition

Shelves: science, non-fiction

Quantum Mechanics: The Theoretical Minimum is the second book in the Theoretical Minimum series. The first book was about classical mechanics, covering both Newtonian and advanced mechanics, and in a way it felt like a preparation for quantum mechanics. Having read this book, I can safely say that quantum mechanics is even weirder than I thought.

The first half of the book moves at a slow speed. In that sense it reminded me of the first book, just introducing the reader to the necessary tools and Quantum Mechanics: The Theoretical Minimum is the second book in the Theoretical Minimum series. The first book was about classical mechanics, covering both Newtonian and advanced mechanics, and in a way it felt like a preparation for quantum mechanics. Having read this book, I can safely say that quantum mechanics is even weirder than I thought.

The first half of the book moves at a slow speed. In that sense it reminded me of the first book, just introducing the reader to the necessary tools and mindset for dealing with quantum mechanics, such as linear operators, eigenvectors, eigenvalues, bra-ket notation, among others. In the second half of the book the speed picks up, though not as much as it did in the first book, as we get introduced to entanglement, and then move on to particle dynamics and the harmonic oscillator. Much like its predecessor, this book does a great job at introducing the reader to the subject (with better editing than the first book). This was the first time I read any kind of book that deals with the real physics and mathematics of quantum mechanics, so I don’t know how other books deal with it in this aspect. I can only say that the way the authors prepare the reader for what’s coming up is quite remarkable.

I didn’t remember much of the linear algebra that I had previously learned. The authors do a great job at introducing the reader to this topics. This happens when we get introduced to linear operators, eigenvectors and eigenvalues. I also quite liked the way the authors made the transition from using algebra to using differential equations in the second half of the book, as we get introduced to particle dynamics. Also on a side note, when I was a student at university I was taught that spin is sort of the quantum analog of classical angular momentum, but not really. At the time I found it rather confusing. I’m glad Susskind chose a different route.

It’s quite remarkable that someone who’s not a physicist, nor studying to become one, can read this book and come out of it understanding some parts of quantum mechanics. I can’t recommend it enough to other readers with some mathematical (linear algebra and calculus) and physical background who want to dig a bit deeper than the usual popularizations of quantum mechanics. It presents a step from popular science books to textbooks. Just make sure you read the first book before, as it introduces some key concepts that play a major role in quantum mechanics [hi commutators]. I can’t speak for physicists in terms of this book, though I have a feeling it might be an enjoyable read for such reader. The only downside I see in this book is that it may seem somewhat disconnected from experiment and its history due to the double-slit experiment, photoelectric effect and others not being mentioned.

In summary: while I might have enjoyed more the previous book, mainly because classical mechanics is less abstract than quantum mechanics and easier to digest, how I wish that all those textbooks I read in university were this fun. I will soon be reading the next book in the series on Special Relativity and Classical Field Theory. ...more

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Jan 10, 2015 Roy Lotz rated it really liked it

Shelves: ignorance-of-experts, education, over-my-head

We could, of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact, mathematics is, to a large extent, invention of better notations.

—Richard Feynman

I’m a bit sad to be finally putting this book down. Now, I can no longer tell friends and coworkers that I’m reading a book about the mathematics of quantum mechanics. Oh well.

I’ve already written a fairly detailed review of the first volume (which can be found here); and since this volume is very s ...more

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Apr 26, 2014 Ivan Vuković rated it it was amazing · review of another edition

Shelves: physics, informal-but-technical

Susskind's Theoretical Minimum series might not be everybody's cup of tea, but I'm really beginning to love this style (way more than the video lectures, I should add!).

It's not your usual popular science with so much hand waving and analogies it almost feels like patronising, but it's not the usual cold and formal textbook style either.

Susskind manages to explain all the core ideas of the theory in a beautiful and coherent way. Some details must, of course, be omitted, but there's no BS and swe ...more

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Mar 29, 2014 Ry rated it really liked it · review of another edition

Shelves: sciencey-stuff

Great introduction to the subject giving a very insightful depth to linear algebra. Unlike most books for quantum mechanics this book requires that you have some fundamental knowledge. This brings me to my first issue. For some reason it is expected of you to have read the earlier book published about classical mechanics, although my training in this has come from other means fortunately; people buying this book separate from the other theoretical minimum series without training in classical dyn Great introduction to the subject giving a very insightful depth to linear algebra. Unlike most books for quantum mechanics this book requires that you have some fundamental knowledge. This brings me to my first issue. For some reason it is expected of you to have read the earlier book published about classical mechanics, although my training in this has come from other means fortunately; people buying this book separate from the other theoretical minimum series without training in classical dynamics will be out of the loop. Though he is not heavily reliant on the first volume the references to it make it feel like a cash grab rather than a means of educating.
One of pleasantries about this book is that it covers the mathematics of entanglement with sincerity and without being patronising. The author is aware that this is most probably your first time tackling such concepts (at least numerically) and treats the phrasing and layout with care as to minimize the confusion caused by the complexity of the subject. Which allows me to elaborate on my second gripe, the ambiguity and abstractions of quantum are made vehemently clear throughout the book, stating how certain numbers don't have physical meaning. This left me shaky on my understanding so I never felt truly confident in my abilities; I attempted the exercises in the book. I believe I got them right, but there are no answers, neither in the book nor online (that I could find). In a classical dynamics module or calculus based topic I wouldn't mind so much as examples of these present themselves far more commonly, however in relation to how ambiguous the subject is some workings on proofs would not go amiss to help my understanding (at least answer half the problems). I understand that being reliant on some answers doesn't prove you know the information, but without answers I will never know; this also seems a problem as readers new to mathematics may need this confirmation to give stability to their understanding.
Ignoring the uncertainty in some parts of the book, this is definitely a well articulated text allowing the more developed reader to hone their skills in QM. I will most probably read this again both as a fun read and as a reference :D ...more

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Feb 07, 2016 Galen Weitkamp rated it it was amazing

Spooky Action at a Distance by George Musser
and
Quantum Mechanics the Theoretical Minimum by Leonard Susskind and Art Friedman

review by Galen Weitkamp

Perhaps it’s unfair to compare these two works given the differences in the intent of their authors. George Musser is fascinated by what some identify as the nonlocal nature of the measurement process in quantum theory. It seems to this reader that his intent is not only to inform but to convince the reader of its “reality” and the consequences that ...more

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Oct 09, 2017 Alexandra rated it really liked it · review of another edition

Shelves: unfinished, non-fiction

I am putting this book on hold for now. I started reading it during a long voyage and it was very interesting and invigorating, like a good workout for the brain. But as soon as I got back to work, I lost the stamina necessary to keep up with the book.
It is hard. The math is real and you have to learn a whole new vocabulary to follow the explanations.
But even if I read only a half of this, I got what I wanted originally. My big question to quantum mechanics was something like "Don't they see ho ...more

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Jul 05, 2015 Woflmao rated it really liked it · review of another edition

Shelves: reviewed, science

The motivation for this book is to explain the fundamental ideas of quantum mechanics (QM) in such a way that readers with very little mathematical knowledge (some calculus, vectors in 3-space) are able to understand it. In this, the book is mostly successful.
As someone with a broader mathematical background who learned some QM before, I was mostly interested in the pedagogical angle the book would take. Most physics books introduce QM from a historical point of view, reviewing the problems lead ...more

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May 16, 2014 Chris rated it it was amazing

Shelves: nonfiction, science

Excellent, effective, and entertaining. Compared to the first volume, The Theoretical Minimum: What You Need to Know to Start Doing Physics, this one has much more accurate editing and typesetting, along with a better co-author. This series of books is destined to be classic. ...more

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May 31, 2014 Dale rated it it was amazing

Shelves: science, mathematics, favorites

An excellent continuation of The Theoretical Minimum, which is a prerequisite to reading this book.

I say here that I've "read" this book, but so far I've only skimmed to get the lay of the land. Because this is not a bullshit popularized treatment of quantum mechanics, it takes actual work and concentration to make your way through it and really understand the mathematics. So this is going to be my background reading for some time to come. ...more

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Jan 02, 2015 G.R. Reader rated it liked it · review of another edition

Susskind shows you how beautiful quantum mechanics is. He does a great job - it's almost impossible to believe that something as cool and elegant as this wouldn't be true. Well... string theory is even cooler and even more elegant, so that must be true too. You see?

Okay Len, nice try. But I wasn't born yesterday.

...more

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May 12, 2016 William Schram rated it it was amazing

Shelves: mathematics, science, non-fiction, physics

This book is a continuation of The Theoretical Minimum which covered Classical Mechanics in physics. Using simple language and explaining the terminology, Susskind and Friedman go through the basics of Quantum Mechanics. They talk about eigenvectors and eigenvalues, bra-ket notation, wave forms, uncertainty and linear operators. Even more is covered, but you get the basic idea I hope.

This book leaves some things to the reader, for instance, you might have to prove some sort of mathematical theor ...more

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Apr 29, 2014 Alex Nelson rated it it was amazing

Shelves: physics

Considering this was written for a lay audience (or, perhaps more accurately, a mathematically savvy but not-too-knowledgeable audience), it's quite a remarkable book.

The focus is on finite dimensional systems (i.e., quantum information) initially. This is a similar approach, if I recall correctly, that Isham takes in his Lectures on Quantum Theory: Mathematical and Structural Foundations.

Susskind nicely avoids the problematic terminology physicists have with dimensions. The free particle in one ...more

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May 07, 2016 Morgan rated it it was amazing

This is a fantastic introduction to quantum mechanics. It goes over vector and wavefunction formalisms, and discusses almost all the math you need to understand (you'll need calculus before reading this book).

The book starts from a discussion of electron spins, and develops quantum mechanics to explain how spin changes on measurements or if placed in a magnetic field. The Schroedinger equation is derived and explained, and then applied to harmonic oscillators in general.

This book is engaging, we ...more

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Jun 20, 2014 Christel rated it it was amazing

Leonard Susskind puts quantum mechanics in the most entertaining and relatable terms. All you need to understand all this is calculus, linear algebra, statistics and probability. I haven't got all my linear algebra down, but so far haven't run into anything I couldn't figure out within 5 mins of googling. ...more

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Mar 18, 2014 Jeremy Sawruk rated it it was amazing

Shelves: physics

Good followup to my Stanford course on quantum mechanics.

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Jun 15, 2020 Sayed H Fatimi rated it it was amazing

A deeply succinct introduction to the world of Quantum Mechanics, the foundations that govern our world, and the basis on which future discoveries of physical laws will be built. Leonard and Art do a wonderful tribute to the big players of the late 19th - early 20th century from Maxwell to Einstein, and my personal favourite, Paul Dirac; whilst I believe having a precursory knowledge of the mathematics involved is useful, with the structure of the literature involved it is not entirely necessary ...more

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Oct 03, 2018 Myat Thura Aung rated it it was amazing

Never thought learning the essentials of quantum mechanics would be this easy. It's probably because I'm a math student tho, and sadly it might be challenging for those who are not so familiar with maths. (But hey, the series do introduce you to the mathematical concepts that you need to know.) I think I can safely say that this serves as the most acccessible introductory text on quantum mechanics. ...more

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Jun 13, 2020 Revert marked it as did-not-finish

DNF at page 64. I tried I really did. My brain just isn’t cut out for a book that is clearly written for people much smarter than me.
If anything, I’m now convinced that Physics isn’t the A Level subject for me. I’ll probably choose History instead.

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Aug 07, 2020 Alex Telfar rated it it was ok

I didn't like this book.

I think it approches teching QM entirely the wrong way.
- They start from math and show that it can be used to describe QM. This seems backwards to me. We should learn about quantum phenomena, the data, and then stumble on some math than can help us describe that data.

Also, I think their interpretation of QM doesn't make any sense.
- Waves of probability, spin just 'is', entanglement and spooky action at a distnace, observables are treated differently, ... I mean come on.

Bu ...more

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Feb 09, 2020 Julian Schrittwieser rated it it was amazing · review of another edition

Approachable introduction to Quantum Mechanics, assuming you are comfortable with some mathematics. I especially liked the explanation of measurement apparatus vs system under measurement, and how one way of viewing a measurement is to say that the apparatus becomes entangled with the system!

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Jun 23, 2018 Molino rated it it was amazing · review of another edition

Shelves: read-in-english, physics, favourite-non-fiction

4,5. An educational beginning and a fantastic introduction to quantum mechanics but it certainly makes your head spin!

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Apr 14, 2014 Brian Clegg rated it liked it · review of another edition

I saw this book on the shelves in my local booksellers which are usually reserved for books which are new, interesting and likely to sell a lot of copies. They were right on two out of them, but they were in cloud cuckoo land on the ‘lot of copies’ part (unless we get a ‘Brief History of Time effect’ where lots buy it and don’t read it). This is a new and interesting book, and for the niche it is aimed at it is brilliant – but that is a narrow niche indeed.

Usually there are two kinds of science I saw this book on the shelves in my local booksellers which are usually reserved for books which are new, interesting and likely to sell a lot of copies. They were right on two out of them, but they were in cloud cuckoo land on the ‘lot of copies’ part (unless we get a ‘Brief History of Time effect’ where lots buy it and don’t read it). This is a new and interesting book, and for the niche it is aimed at it is brilliant – but that is a narrow niche indeed.

Usually there are two kinds of science books. Popular science explains what the discoveries and theories of science, with historical perspective, so that the general reader can get a feel for them – but reading a popular science book on, say, quantum mechanics would not leave you able to solve quantum mechanics problems.

Textbooks, on the other hand, teach the actual science itself, usually with a lot more maths, so that you can indeed do the workings, but they don’t give you any context, and they are inaccessible (and, frankly, highly boring) to most readers.

This book highlights a tiny crack in between the two, a niche where it can do a very interesting job of leading the reader into the actual science, but in a more hand-held and less boring way than a textbook. Because it takes this approach it hasn’t got the context or readability of a popular science book – but it’s far more readable than a textbook. Similarly, it doesn’t have quite enough detail to really ‘do’ the physics – but it takes you well on the way there, so that it would only take a little textbook work to get on top of it.]

The only thing I’d criticise (apart from the narrowness of that niche) is the really irritating attempts at folksy fictional openings to the sections. They don’t work. Stay with what you’re trying to do, guys, don’t try to be entertainers.

For most popular science readers this book simply won’t work. It makes the infamously ‘I started it but couldn’t finish it’ Brief History of Time look highly simplistic and non-mathematical. And for serious physicists, it’s still too limited – though it takes what is in some ways a better approach, giving more emphasis early on to entanglement, than the way quantum physics is traditionally taught. Either for those about to start a university physics course who want some preparation, or for someone who finds popular science explanations too summary and is prepared to take on some quite serious maths (A level maths required as a minimum, I would say) it’s a fascinating addition to the library. For the rest of us, probably best to leave it where it is. ...more

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Jul 11, 2019 Nathan Velson rated it it was amazing

Once again, the Theoretical Minimum takes you past the pop-science to take a real look at the mathematical foundations of physics, in this case quantum mechanics, building on the formulation of classical mechanics from the first book. And once again, for someone who has learned a bit about quantum mechanics in various school/work contexts, I was surprised how much more there was to it than I was aware.
I get a feeling that a lot of introductory physics courses teach QM in the order that it was d ...more

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May 20, 2016 James F rated it really liked it

The sequel to The Theoretical Minimum, which dealt with classical physics, this book explains the basics of quantum theory in a simple (but not oversimplified) way beginning with spin states and working through the Schrödinger equation, combinations of states, entanglement, and the uncertainty principle. The first half of the book introduces the mathematics of complex vector spaces in a very understandable way (I had never studied linear algebra at all, even with real vectors, and I had no troub ...more

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Dec 31, 2014 Richard Thompson rated it it was amazing

Shelves: physics

I have read a lot of popular physics books that left me feeling vaguely unsatisfied. Finally I have found a book that I can almost completely understand that does not pull any punches. It was sometimes a slog to get through the material, and I will probably have to do some additional reading before it all completely sinks in, but now I finally feel that I have the grounding to be able to move on to higher level material. There is a bit of hand waving in the math in this book, which bothered me a ...more

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Oct 07, 2015 Neelakantan K.K. rated it really liked it · review of another edition

Shelves: art-friedman, theoretical-minimum, leonard-susskind, quantum-mechanics, physics, non-fiction

Great book but becomes difficult fairly quickly. Be prepared to read sections over and over again to understand some of the concepts better. Presented very well, but some bits could have done with a bit more explanation. The notation could also be clearer in some areas which would have reduced the difficulty a bit. I haven't read Volume I on classical mechanics yet, and maybe reading that first would have made it a bit easier to follow things here but it doesn't hamper understanding. Also, a pri ...more

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Jul 26, 2015 Tassos added it · review of another edition

Shelves: technical, science

Wow, that has been a very nice journey. This book is not an easy job, especially if your physics definitions are a bit rusty. But it is definitely a self-contained and you need very little to go through it. The only things you need is courage, persistence and an open mind for grasping new way of thinking.

This is really a great introduction to fundamental Quantum Mechanics, which might allow you to go deeper in the field and sub-fields. However, it is just the current state of how QM is described ...more

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About Leonard Susskind

Leonard Susskind

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Leonard Susskind is the Felix Bloch Professor of Theoretical Physics at Stanford University. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Phys ...more

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Theoretical Minimum (3 books)

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“world seems filled with people who are genuinely, deeply interested in physics but whose lives have taken them in different directions. This book is for all of us.” — 1 likes

“The units that we use reflect our own size. The origin of the meter seems to be that it was used to measure rope or cloth: it’s about the distance from a person’s nose to his or her outstretched fingers. A second is about as long as a heartbeat. And a kilogram is a nice weight to carry around. We use these units because they are convenient, but fundamental physics doesn’t care that much about us. The” — 0 likes

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