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Quantum Mechanics: The Theoretical Minimum, by Leonard Susskind
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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 New York Times best-selling The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics' weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind's eponymous Stanford University-hosted continuing education course.
An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.
- Sales Rank: #2117229 in Books
- Published on: 2015-02-25
- Original language: English
- Dimensions: 7.80" h x .87" w x 5.08" l, .68 pounds
- Binding: Paperback
Review
“The writing is fresh and immediate, with plenty of detail packaged into the smooth narrative.... [O]n their own terms, I found Susskind and Friedman's explanations crisp and satisfying.... I maintain a clear recollection of the bewilderment with which I struggled through my own university quantum-mechanics courses. For students in a similar position, trying to draw together the fragments of formalism into a clear conceptual whole, Susskind and Friedman's persuasive overview—and their insistence on explaining, with sharp mathematical detail, exactly what it is that is strange about quantum mechanics—may be just what is needed.”
—David Seery, Nature
“[T]he book will work well as a companion text for university students studying quantum mechanics or the armchair physicists following Susskind's YouTube lectures.”
—Publishers Weekly
“This is quantum mechanics for real. This is the good stuff, the most mysterious aspects of how reality works, set out with crystalline clarity. If you want to know how physicists really think about the world, this book is the place to start.”
—Sean Carroll, physicist, California Institute of Technology, and author of The Particle at the End of the Universe
About the Author
Leonard Susskind has been the Felix Bloch Professor in Theoretical Physics at Stanford University since 1978. He is the author (with George Hrabovsky) of The Theoretical Minimum, as well as The Black Hole War and The Cosmic Landscape. He lives in Palo Alto, California.
Art Friedman is a data consultant who previously spent fifteen years at Hewlett-Packard as a software engineer. A lifelong student of physics, he lives in Mountain View, California.
Most helpful customer reviews
12 of 12 people found the following review helpful.
A Mind Tingling Challenge – Learn Quantum Mechanics
By Malcolm Cameron
Physics lectures are of three types according to this anecdote of Niels Bohr:
“A young man was sent by his own village to a neighboring town to hear a great Rabbi. He was to bring back a report in which all could share. When he returned he told his eagerly awaiting fellow citizens: “The Rabbi spoke three times. The first was brilliant; clear and simple. I understood every word. The second was even better, deep and subtle. I didn’t understand much, but the Rabbi understood it all. The third was by far the finest; a great and unforgettable experience. I understood nothing and the Rabbi himself didn’t understand much either.”
Professor Susskind (1) of Stanford University is far ahead of Bohr’s Rabbi – he understands it all. To Susskind “Everything is easy in Quantum mechanics” (2). So easy that he always “destroys his lecture notes to prevent his lectures being the same next time” (3).
“Given enough time, with no distractions, you could use [his book (4)] to eventually master Quantum Mechanics” (5). An attractive challenge as the book is only 350 pages.
Only 350 pages perhaps, but it assumes you are versed in Classical Mechanics (which you aren’t). Realistically, you need Susskind’s first book (6) plus a preliminary YouTube series of 9 x 1.5 hour lectures on Quantum Entanglement (7). Plus you will need assistance from 10 x 1.5 hour YouTube lectures (8) in parallel with the book. Still a realistic challenge given the results (9).
According to Susskind, Quantum Mechanics is much more fundamental that classical physics. “As far as we know quantum mechanics provides an exact description of every physical system” (10). Moreover, “the logic of classical mechanics of Newton is incorrect, the underlying structure is inadequate” (11). Not only should we logically learn quantum mechanics first, it is technically much easier than classical mechanics (12).
Susskind lives in a Quantum Mechanical world, the real world, deploring our choice of units that makes Avogadro’s Number (13) and the speed of light (14) ridiculously large and Planck’s Constant (15) ridiculously small. He blames historical chemists who measured things by comparison to the size of their hands. Choosing units appropriate to the sub-atomic scale, such as making Planck’s constant = 1, would make his world feel normal.
For those who enjoyed science and mathematics to a reasonable level (16) but who had to follow a career to survive in the world, this is more an opportunity than a challenge. Not that it is not a challenge! It is a mind tingling challenge. A way of familiarizing with the real subject with the actual equations - not a popularization.
The fascinating history of Archimedes, Johannes Kepler and Isaac Newton fitting an ellipse to the Mars orbit and concluding with the Law of Gravity is only the half of it. Understand how the mathematics of vectors and matrices are fitted to the real world being Quantum Mechanics. Like Archimedes the French mathematicians Joseph-Louis Lagrange, Siméon Poisson, and the Irish mathematician William Rowan Hamilton were nice enough to magically or inadvertently provide the mathematics a long time prior to make it possible. Why this mathematical physics works no one knows, neither Susskind nor the Rabbi.
One moment you feel like like Niels Bohr’s student in his third lecture then you are stunned when Professor Susskind commences a short summing-up by saying, in a matter-of-fact way, that an equation derived in the lecture is called Schrödinger’s equation (17)! Or that the postulates he has been talking about are Dirac’s postulates of Quantum Mechanics formulated in the 1930’s which have never needed to be replaced (18). Or, early on, describes a vector and says that it is Dirac’s notation (19).
Finally, Susskind is to be applauded. If this can be done with Quantum Mechanics, it can be done in any subject of Physics or Mathematics or any other area of study. There must be a value in doing this (other than ex-auto workers retraining themselves for jobs at CERN) as the work will inevitably not continue to be publically funded unless tax-payers have some idea what it is.
PS: The advantage of a career outside Physics is to know “you always write the minutes before the meeting”. Bohr’s student may finally have understood so little that he was not game to return to his village. As a precaution I have written this travelogue well before completing the trip.
(1) Leonard Susskind is the Professor of Theoretical Physics at Stanford University, and director of the Stanford Institute for Theoretical Physics. His Wikipedia entry is a good read in itself.
(2) Lecture 9, Quantum Entanglements
(3) Lecture 9, Quantum Entanglements
(4) Quantum Mechanics – The Theoretical Minimum by Leonard Susskind & Art Friedman. The “minimum” means just what you need to know to proceed to the next level.
(5) Science News: quote from back cover of Susskind’s book.
(6) The Theoretical Minimum – What you Need to Know to start doing Physics Leonard Susskind and George Hrabovsky.
(7) Quantum Entanglements, Susskind, Stanford University, YouTube. It seems that the old unadorned lecture format has stood the test of time with only the whiteboard and marker (when it works) replacing the blackboard and chalk.
(8) Modern Physics, Quantum Mechanics, Susskind, Stanford University, YouTube.
(9) Well, you did not expect to read 350 pages straight cover to cover and then know Quantum Mechanics, did you? This is a 6 to12 month project – reading, watching YouTube lectures, frantic note taking hoping you might understand it later (the iPad pause button being a luxury unavailable in university lectures), revision, pushing forward, retreating, then finally with your newfound knowledge applying for a job at CERN.
(10) Page xix.
(11) Lecture 1, Quantum Mechanics
(12) Page xx.
(13) Avogadro's number, number of units in one mole of any substance (being its molecular weight in grams) ≈ 6×1023.
(14) Speed of Light: c ≈ 3×108 m/s.
(15) Planck’s Constant: The energy contained in a photon, the smallest possible ‘packet’ of energy in an electromagnetic wave ≈ 6.6x10-34 joule-seconds.
(16) Realistically, for those who think they know classical Newtonian Physics and remember studying vectors and matrices, exponentials such as eiθ = cosθ + isinθ and who once knew the expansion of sin(θ + Φ).
(17) Lecture 9, Quantum Entanglements
(18) Lecture 4, Quantum Mechanics
(19) Page 11, Quantum Mechanics – The Theoretical Minimum
Malcolm Cameron
8 May 2016
34 of 36 people found the following review helpful.
Flawed by lack of worked out answers for excercises.
By Leeber Cohen
Professor Susskind's lecture series on You Tube are very popular and he deserves our thanks for his efforts. It is also wonderful that there is an audience that wishes to learn these subjects. It is assumed that you know linear algebra and complex variables. If you have not had these subjects or need a refresher, you will have a better time with this book if you study or review these subjects. I would recommend the Cliff Quick Review of Linear Algebra by Leduc and Chapter 1 of Schaum's Complex Variables 2nd edition by Spiegel. They both have many worked out problems and the books are inexpensive.There are more expensive alternatives like Engineering Mathematics by Stroud or Shankar's Quantum Mechanics textbook which cover these areas. Susskind makes heavy use of spin and the Pauli Matrices as a basic model for quantum mechanics. A similar approach was taken in Jordan's Quantum Mechanic in Simple Matrix Form published in the 1980s and available on Dover. Susskind is a good teacher and further simplifies the math, probabilities, commutators, and operators to make the subject more easy to follow. The introductions to the Heisenberg Uncertainty Principle, Schrodinger Equation, and Entaglement are nicely done and are a good read. If you want to learn some concepts of basic Quantum Mechanics and are not adverse to the math described this book will fill that need. Learn or review the mentioned math first or you will be lost quickly. You need to know what a complex number is,why we need complex numbers, how to obtain a complex conjugate, and Euler's famous formula. Susskind covers this in three short pages which is unlikely to mean much to you if you do not remember or know the math. It will also help to watch the lectures on You Tube. The major flaw of the book is the excercises. They range from easy to hard. The answers are not provided and the techniques for answering them should be fully worked out. This should have either been added as an appendix to the book or posted on the web. These excercises are meant to test and rewire your brain. They are important teaching tools but most of us do not have teaching assistants to check our answers and help us when we are lost. What may be obvious to the teacher is frequently not obvious to the rest of us. I have taken off one star for not have a longer chapter on the math required. I have also taken off a star for the lack of answers (worked out would be even better) for the excercises.
8 of 8 people found the following review helpful.
THEE quantum book + Solutions available online
By J. Canada
I've been working through this book. I learned quantum in my undergrad years from the Tannoudji book. It was very dry and I spend most my time trying to figure out what he (Tannoudji) was trying to say, THEN figure out whether I can prove it, etc. Funny how really smart people can create creatively new ways to make stuff more difficult through weird explanations.
This is not so with Susskind. Susskind writes like Feynman: clear explanations on complex topics. I assume he's a native english speaker, as his tone is very colloquial and uninimtidating. He assumes the reader knows nothing of quantum and explains things in bit-sized pieces which are easy to digest. He rarely says things like "well OBVIOUSLY this flows from this" (when the things are so obvious).
Anyways, the book is a bit unorthodox. It starts off talking about spin states and vector spaces. This is different than the typical quantum books that start off with talking about solving the Schrodinger equation. Which, now that I think about it, isn't really a great place to start. It's a wave equation that's only once-piece of the bigger picture.
The result is a book that has a very gradual learning curve.
That said, readers still need a bit of math background if they want to get through this book. I'd say at least a decent understanding of complex numbers and matrix algebra are a prerequisite. Both those subjects are thoroughly explained in places online (Khan Academy) for free.
SOLUTIONS:
I read another reviewer rate the book low because there is a lack of worked out solutions. That I disagree with.
Google search "Quantum theoretical minimum solutions" and they will pop up. There are several unofficial sites out there that have answers to the solutions. For instance, google search "the uncertain biscuit quantum" or "chris brittain quantum". The solutions are out there.
Also, on that note, the problems in this book are few..but concise and great. Very on-point.
Regarding the reviewers who are rating this book low b/c it's too difficult. That's not really a good reason to rate a QUANTUM book low. For two reasons (1) it's a quantum book for christsakes. it is by far the most math-friendly book written on the subject. reading about quantum mechanics without math is not "doing" physics..it's just cataloging knowledge (e.g. stamp collecting), (2) how can you rate a book low if you don't understand it? What are your reviewing parameters?
If you have a little complex number knowledge and rudimentary matrix operations (e.g. matrix multiplication, etc.) under your belt, you'll be fine.
The Kindle version is fine. That's what I bought (I have a paper copy too). I prefer the kindle version because I can read it on my phone while waiting in line, etc. The equations come out fine (I'm not sure what the other revieweres were complaining about, I'm reading it on my iPhone 5s just fine.)
If you know nothing of quantum and want to learn, I highly HIGHLY recommend this book.
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