Quantum Mechanics: The Theoretical Minimum by Leonard Susskind (PDF)

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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.

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⭐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 ≈ 6.6×10-34 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 MinimumMalcolm Cameron8 May 2016

⭐This book is designed to meet the needs of a mathematically inclined reader. An undergraduate level physics textbook is perhaps too advanced, and a popular book with no math discusses the principles of quantum reality that is easier to understand, but this book is at the middle level of complexity. This is meant for readers who are interested to know the equations that describes the mechanics of fundamental particles in terms of their position, motion, and energy in spacetime. Math tends to make certain things easy to put in perspective than mere descriptions without equations! The readers are expected to know mathematical concepts such as complex numbers, vector spaces, linear operators, and tensor products, all of which are artistically explained in a series of interludes. Specific concepts of the space of states, time evolution, principles of uncertainty, and quantum entanglement are described at moderate level of complexity, and yet reader-friendly. I recommend doing the exercises at the end of each chapter. I could not answer many of these questions, but it certainly makes you think. That is a learning process.The biggest challenge is the understanding quantum entanglement because there is no classical analog for a system whose full state description contains no information about its individual parts, and nonlocality (two particles separated at large distances) is difficult to define. The best way to come to terms with these issues is to internalize the mathematics.Two principles emerge as fundamental, the spin state of quantum particle or qubit. In classical physics, everything can be built out of yes/no (1 or 0) questions. Similarly, in quantum mechanics, every logical question becomes a question about qubits (basic unit of quantum information, two level quantum system, spin up or down, both in a state of superposition). The second principle is the harmonic oscillator. How do particles move in quantum mechanics? We know that fundamental particles have wave-particle duality. It exists in both wave and particle forms. Then how do matter in its wave state can have gravity associated with it? That makes understanding quantum gravity harder. In addition, waves oscillate much like a mass attached to the end of a spring. The oscillators, not masses attached to springs, are imagined as waves, in fact they are the oscillating electric and magnetic fields. For each wavelength, there is a mathematical harmonic oscillator describing the amplitude or strength of the field. For many waves there is a lot of harmonic oscillators all running simultaneously. Fortunately, they all oscillate independently. The higher-energy wave functions oscillate more rapidly and are more spread out. This is the consequence of quantum field theory. Another question is how do quantum states change with the evolution of time? They change so that information describing the system are never erased. This is one of the most fundamental phenomenon that haunts in describing black holes.This book sticks to the simplest possible quantum system, one with a two-dimensional state space. The algebra is developed from scratch and author Leonard Susskind describes at a very leisurely pace and the quantum reality is described in the simplest context.

⭐This book will appeal to people who, like me, have dabbled in many ways with quantum theory over the years and read many books on it but perhaps never before found anything so clear, authoritative, mathematically sound, and free of blather about how quantum theory defies what seems to pass for common sense along lay readers. The mathematical level will challenge readers lacking prior acquaintance with algebra, calculus, vectors and matrices, complex numbers, and classical mechanics, but this is after all the basic toolkit for anyone seeking to get a serious grip on what makes quantum mechanics tick. Apart from that, the humility that comes with advancing age and a wry sense of humor will suffice to carry you through this engaging little book.Leonard Susskind obviously knows the theory as well as anyone, intimately, and has evidently taught it often enough to know exactly know to optimize his approach. He prepares the ground carefully and uses the qubits representing spin as his main running example, which lets him avoid murky issues around particles and waves for most of the discussion. He also works in Dirac algebra from the start, which is far and away the clearest approach for my money and provides a solid base to discuss the respective approaches and main results of Heisenberg and Schrödinger, when he gets that far. I found his treatment far more enlightening than that in volume 3 of the Feynman lectures, where Feynman made a mess of presenting Dirac algebra and failed to motivate either matrix mechanics or wave mechanics with sufficient mathematical or philosophical care.Susskind has properly taken on board the depth of the foundation work needed to present quantum theory intelligibly, so as not to be shipwrecked on the rocks of the paradoxes that lead weaker heads to despair about ever making sense of their challenge to what used to pass for common sense about physical reality. His discussion of states and state vectors, basic principles, entanglement, uncertainty, nonlocality, dynamics and so on is always spot on, with a confident mathematical grip on the issues and a calm refusal to be ruffled by the difficulties they present to intuitive comprehension. His approach is ideally suited to showing how and where quantum logic defies classical logic, how far you can go before deep issues about spacetime need to be confronted, for example by going from discrete sums to continuous integrals, and how little you need to fuss about particle and waves before the new foundations are in place.A modern introduction to quantum mechanics needs to go beyond Dirac’s elegant but dated and difficult textbook, both in terms of approach to set things up for new work in quantum computation and high energy physics and in terms of content to touch on such topics as the Bell inequalities, the trials of Alice and Bob, and the creation and annihilation operators of quantum field theory. Susskind does all this with masterly cool, as well as a warm appreciation of the excitement in wait for people who go on to tackle those further topics. Art Friedman has made sure the text remains accessible to plodders like me, though perhaps some of his humorous additions might be trimmed or deleted in future editions of what seems to me to be a core text with a long and glorious potential afterlife.

⭐If you work through this book carefully, you will learn some of quantum mechanics — a similar subset to what the Feynman lectures would give you, but without the atomic physics. You will learn a lot about spin 1/2 and entanglement of two particles. You will learn about one dimensional Schrödinger and how to solve it in free space and also the harmonic oscillator.You won’t learn anything about bosons versus fermions, or anything at all about three dimensional solutions or anything about the Hydrogen atom or nucleus.You will not be able to follow the book unless you understand basic calculus and some of classical physics, such as the formulae for kinetic energy, momentum and the energy of a spring — basic A level stuff. Though integration by parts is spelled out for you.The book is aimed at quite a low level, it works very slowly and step by step, and it is reasonably rigorous. I particularly like the presentation of entanglement and the non nonsense approach to the interpretation of quantum mechanics. It would be hard to read this book and end up thinking that consciousness, mysticism or wave-function-collapse have anything to do with quantum mechanics.This book leads you to Many Worlds by the back door, without ever making that explicit, but I don’t see that as a bad thing. At the moment, it is the only consistent theory out there.There are a very few typos in the text, but rather more in the exercises. The exercises are mainly very easy, but a few are difficult and a few do not make sense at all, because of mistakes in them. A little more proof reading would help here.I read the Kindle version as it is cheaper. It’s OK, but a bit of a pain to leaf back to find formulae that are referred to. I much prefer the way this is done in the online Feynman lectures, where formulae pop up in a box when you click on them.Overall, I recommend this book. If you’ve not done any quantum mechanics before you’ll find it pretty hard going, but probably no harder than any of the other books out there and easier than many of them.

⭐These series of books are by far my favourite science books. Ever. Having read the classical mechanics book, I was extremely excited when this was released. I would warn though that it is not for the light-hearted. The Theoretical Minimum books are filled completely with equations and if your mathematics isn’t up to scratch you wont get past the second lecture.Having said this, if you wan’t to start understanding science; real science that is, not like the science of pop science books where you’re told a few vague ideas and some rough history. Rather, this book takes you into the mathematical framework of quantum mechanics and allows you to do the calculations and discover the true beauty of the equations.Before reading this book my background in mathematics and physics were as follows: GCSE and AS level maths and physics, had read the first book. I don’t think you will struggle to read this provided that you’re willing to work fairly hard at understanding what’s going on and that you have a working knowledge of calculus and a basic knowledge of matrix operations and knowledge of complex numbers.The book covers a variety of topics and by the end of it you will understand the basics of the Schrödinger equation, general uncertainty, the Heisenberg uncertainty principal, using quantum mechanics to calculate probabilities of certain outcomes and also quantum entanglement and why it’s such a strange phenomena. These ideas are not made readily available, you will have to do a fair bit of work in understanding in order to fully appreciate these ideas.It took me about 3 months to read and understand this book and I feel that I have a basic grasp on some fundamental ideas in quantum mechanics. If you have no serious understanding of the maths of physics or have no interest in learning it then this book is not for you. If you do not want to have to think about the ideas presented in order to grasp their importance then this book is also not for you. However if you want an invitation into the world of real quantum mechanical theory then this is the book for you.

⭐I do recommend this book. The authors did a great job in explaining QM in an accessible manner in a lively language. It does contain some mathematical manipulations but nothing too striking. The book has some exercises inside but again, not hard or involving.Overall, I’d recommend this book to a complete newcomer to quantum mechanics. If you have some experience with QM, I’d guess you can skip it safely.If you want to build a good working knowledge of Quantum Mechanics I recommend the following:1) Read this book first, it’s a nice introduction.2) Read Dirac’s book – The Principles Of Quantum Mechanics3) Read a university level book such as Binney’s The Physics of Quantum MechanicsNow, after this you’d have gathered nice grasp of QM. But this ain’t enough – go into the applications such as Solid State Physics, Atomic Physics, Nuclear… Only when you’ve applied the machinery of QM you would “understand it”. Not that anyone can.Get the book ( ͡° ͜ʖ ͡°)

⭐This book is wonderful in the way that it introduces the mathematics of quantum mechanics starting from the point of view of quantum computing, i.e. starting with the quantum bit (the qubit). The mathematics seems to flow naturally from the physics in this book. Leonard Susskind’s online lectures are always excellent, including the Theoretical Minimum series. I should say that this book is well written introductory text (and assumes some basic mathematics, complex numbers and linear algebra), and is neither popular science nor a second course in quantum mechanics. But, as other reviewers have noted, the Kindle edition of this book curtails some equations at the end of the line, and the book in general has a number of minor technical errors. This book is in bad need of an edit, which does sometimes detract from following the text.

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