Rating: 
Summary: A critique of Dirac's book
Review: Dirac's book is the Bible in QM. He is the inventor of bra and ket notation. This is the most difficult and important idea in QM, I think. Dirac explains the bra and ket in his own way. Although this book cannot be a textbook in class. Everyone who hopes to be a theoretical physicist have to read it once in a life.
Rating: 
Summary: An Underappreciated Classic
Review: First, a disclosure: this was my first QM text. That's right. I picked it up as a sophomore in electrical engineering. This could easily have nipped any hope for a career in research. Rather, I was immediately taken by the undeniable elegance of the exposition. (I distinctly recall my first impression of the discussion on page 9 which is exceptionally lucid on the subject of what QM does and does not tell us about quantized fields, because this is something I had already struggled with unsuccessfully.) Moreover, Dirac reduces QM to what it really is: a few remarkable postulates about how Nature is; and a whole lot of linear algebra. Dirac was arguably a mathematician first and asserted, elsewhere, that it is more important that out theories have beauty than truth in the physical world. Anyone who can at least entertain this notion may gain much from this often overlooked classic, largely free of the pedagogically distracting baggage of wavefunctions. One reviewer has noted that the notation is archaic or cumbersome; I must kindly demur.
Rating:
Summary: An Underappreciated Classic
Review: First, a disclosure: this was my first QM text. That's right. I picked it up as a sophomore in electrical engineering. This could easily have nipped any hope for a career in research. Rather, I was immediately taken by the undeniable elegance of the exposition. (I distinctly recall my first impression of the discussion on page 9 which is exceptionally lucid on the subject of what QM does and does not tell us about quantized fields, because this is something I had already struggled with unsuccessfully.) Moreover, Dirac reduces QM to what it really is: a few remarkable postulates about how Nature is; and a whole lot of linear algebra. Dirac was arguably a mathematician first and asserted, elsewhere, that it is more important that out theories have beauty than truth in the physical world. Anyone who can at least entertain this notion may gain much from this often overlooked classic, largely free of the pedagogically distracting baggage of wavefunctions. One reviewer has noted that the notation is archaic or cumbersome; I must kindly demur.
Rating:
Summary: A critique of Dirac's book
Review: I think it's time someone evaluated Dirac's book more critically. Yes, I am in awe of him just like the next physicist, but I think I owe this review to potential buyers of this book. Please note that:1. This book is NOT the bible of QM. It's thin and quite lean. You will not find yourself using it as a reference, since there are much better books out there for that (Messiah, Cohen-Tannoudji, and other epic accounts of QM). 2. This book is, indeed, elegant, but in the following sense: it almost always travels the shortest distance between two points, i.e. teaches you only whatever is necessary for obtaining a certain result, and/or formula. Therefore, its 3. Its first part, which introduces the bra-ket notation, confuses mathematical and physical ideas. For instance, Dirac states "we now make the assumption that there is a one-to-one correspondence between bras and kets", an assumption which is actually unnecessary owing to the Riesz theorem, which assures us that such a correspondence exists. So, who is this book suited for, in my opinion? I think that only an experienced reader who would like to gain insight into the way Dirac understood QM should read this book. Otherwise, my verdict is: forget it, there are much better books out there. If you're starting out, try Shankar. If you're more advanced, check out Sakurai for some good insights. If you're looking for a reference - see above.
Rating: 
Summary: Elaboration upon the previous review
Review: My thoughts on this book... I would elaborate upon "the way Dirac understood QM", since this is wherein lies the primary value in reading this text. No, this book should not be read as an introduction to the subject. Yes, many topics are treated in a manner that would qualify as being terse. What's more, Dirac's writing style can be fairly dry, portions of the opening chapters are a bit tedious, the notation is frequently less than perspicuous, and roughly the last third of the book is more of historical interest than anything else. With all that said, the first seven or so chapters are rightly considered to be classic, and if you've progressed to the point of being able to tackle Dirac, and you understand WHY it is that you should want to, then none of the above difficulties should PREVENT you from doing so. Most people are introduced to QM through the Schrodinger picture, which is useful for building an intuitive feel for the subject. Unfortunately it also lends itself to picturing things in ways that are a little too classical, and at some point one has to make the transition from imagining actual waves evolving in physical space to the idea of state vectors evolving in Hilbert space. Dirac's transformation theory approach is an ideal tool in this regard, and THAT is why you read Dirac's book. You can also find out about delta functions and the operator approach to the HO problem from the horse's mouth, the chapter on perturbation theory is quite good, and there is a frequently cited section on the motion of wave packets. At the right time and given the correct motivation, this is a good book.
Rating:
Summary: A generalized approach to quantum theory
Review: The purpose of Paul Dirac's "The Principles of Quantum Mechanics" was to bring into an extremely valuable theory, but a dirty theory a decidedly unifying mathematical elegance. This has been wonderfully achieved. For a serious student this book is an excellent place to begin. Dirac in this had to decide on the mathematical form in which quantum theory could be unified. Any author must decide at the outset between two methods. There is the symbolic method, which deals directly in an abstract way with quantities of fundamental importance, and there is the method of coordinates or representations, which deals with sets of numbers corresponding to these quantities. The second of these methods has usually been used practically exclusively.
The symbolic method, however, seems to go more deeply into the nature of things and to be more amenable to generalization into principles. For example, it enables one to express the physical laws in a neat and concise way, and will probably be increasingly used as it becomes better understood and its own special mathematics gets developed. It was for this reason that Dirac chose the symbolic method introducing the representatives later merely as an aid to practical calculation. This has necessitated a complete break from the historical line of development, but this break is an advantage through enabling the approach to the new ideas to be made as direct as possible. Quantum mechanics as defined by Dirac is the application of equations of motion to atomic particles. It was first shown that atomic particles are subject to equations of motion when Bohr set up his theory of the hydrogen atom. The next big development was made when Bohr's student Heisenberg discovered the need for a non-commutative multiplication. The domain of applicability of the theory is mainly the treatment of electrons and other charged particles interacting with the electromagnetic field. Eventually, a way will be found for adapting the high-energy theories into a scheme based on equations of motion, and so unifying them with those of low-energy physics.
Rating:
Summary: A generalized approach to quantum theory
Review: The purpose of Paul Dirac's "The Principles of Quantum Mechanics" was to bring into an extremely valuable theory, but a dirty theory a decidedly unifying mathematical elegance. This has been wonderfully achieved. For a serious student this book is an excellent place to begin. Dirac in this had to decide on the mathematical form in which quantum theory could be unified. Any author must decide at the outset between two methods. There is the symbolic method, which deals directly in an abstract way with quantities of fundamental importance, and there is the method of coordinates or representations, which deals with sets of numbers corresponding to these quantities. The second of these methods has usually been used practically exclusively.
The symbolic method, however, seems to go more deeply into the nature of things and to be more amenable to generalization into principles. For example, it enables one to express the physical laws in a neat and concise way, and will probably be increasingly used as it becomes better understood and its own special mathematics gets developed. It was for this reason that Dirac chose the symbolic method introducing the representatives later merely as an aid to practical calculation. This has necessitated a complete break from the historical line of development, but this break is an advantage through enabling the approach to the new ideas to be made as direct as possible. Quantum mechanics as defined by Dirac is the application of equations of motion to atomic particles. It was first shown that atomic particles are subject to equations of motion when Bohr set up his theory of the hydrogen atom. The next big development was made when Bohr's student Heisenberg discovered the need for a non-commutative multiplication. The domain of applicability of the theory is mainly the treatment of electrons and other charged particles interacting with the electromagnetic field. Eventually, a way will be found for adapting the high-energy theories into a scheme based on equations of motion, and so unifying them with those of low-energy physics.
Rating:
Summary: Don't miss reading Dirac
Review: This book goes all the way back to 1930, the year it was first published, and a time when quantum physics was undergoing rapid development, both in terms of applications and theory. The author was one of the major contributors to these developments, and in this book has outlined his idiosyncratic approach to quantum physics, including relativistic quantum mechanics and quantum electrodynamics.The author's insight into quantum physics is extraordinary and that makes this book unique among the books on the subject. The author introduces immediately the principle of superposition as the tour-de-force of quantum theory in chapter 1 after discussing the inadequacy of classical mechanics in explaining the data on specific heat and atomic spectra. The polarization and interference of photons is used to motivate the principle of superposition, and then the concept of a quantum state. The famous Dirac bra-ket formalism is brought in to give the state concept a mathematical formulation. This is followed in chapter 2 by a mathematical formulation of observables, these being operators that act on the kets, with their adjoints operating on the bras. The eigenvalues of these operators are then the physically realizable results of experiments. The author's discussion on the physical interpretation of this formalism is fascinating and should be read by anyone desiring an in-depth understanding of quantum physics. The formalism up to this point has been purely algebraic, so to apply it to physical problems one needs a representation. This is done in chapter 3, wherein the author also introduces the famous "Dirac delta function". The commutation relations between observables, not of course arising at all in the classical theory, are discussed in chapter 4. The "Poisson bracket goes to commutator" is the theme of the chapter, and one that was followed for several decades, until the advent of the path integral formulation. The Schroedinger and Heisenberg representations make their appearance here, as well as the Heisenberg uncertainty principle. Once the ideas of the preceeding chapters are accepted, there is no turning back on the consequences they entail, some of them quite bizarre at first encounter. This already becomes apparent even when solving for the time development of quantum systems, which is done in chapter 10 for the free particle and motion of wave packets. More applications are treated in chapter 11, such as the harmonic oscillator, and the author shows how to incorporate angular momentum and spin into the quantum theory. He also treats the central force problem, and derives the selection rules for the hydrogen atom. Readers get their first taste of perturbation theory in chapter 12, via the problem of atom in an external electric field. All of these problems illustrate beautifully the ability of quantum physics to fit the experimental data. Particle accelarators were of course coming on to the scene at the time this book was published, and so collision problems are discussed in chapter 13. The important effects of resonance scattering and spontaneous emission are discussed in detail by the author. Even more anti-classical phenomena in quantum physics arise in chapter 14, which deals with systems of identical particles. The description of these is done with symmetrical and antisymmetrical states, and the resulting boson/fermion distinction is outlined and discussed in detail. The author also gives an interesting discussion of permutations as dynamical variables. He constructs a theory for a system of n similar particles when states of any kind of symmetry properties are allowed. The theory does not correspond to any existing particles (and the author acknowledges this), but he uses it as an approximation to a collection of electrons. Permutations are constants of motion in this theory, and for a system of electrons he shows that more than two electrons cannot be in the same orbital state. This "effective" theory of electrons is interesting because in its derivation one sees the explicit need for spin variables, even though spin forces are neglected by the author. This is a neat illustration of the Pauli exclusion principle. In chapter 20, the author develops a theory of radiation, giving a first glance at relativistic quantum theory, i.e. quantum field theory. The theory as he constructs initially however should more properly be called many-body quantum theory, as no explicit "field quantization" is performed, although his result is essentially the same: a collection of quantized harmonic oscillators which he shows to be equivalent to a collection of bosons in stationary states. He applies this theory to the case of a collection of photons interacting with an atom. When describing the interactions between photons and atoms, he then makes the connection with fields, treating the atom first classically and the field of radiation as a vector field. The resulting theory is quantized using the "canonical" approach and the author derives all the now standard quantities, such as the Kramers-Heisenberg dispersion formula for photon scattering. Dirac is well-known for his work in quantum field theory, and he delves into it in the last two chapters. His famous derivation of the "Dirac equation" is given here, but interestingly, he does not refer to the wave functions in this equation as "spinors". He does show the equation is Lorentz invariant, and then studies the electron in a central force using the equation, giving the all-important fine structure of the energy levels. And of course, the theory of the positron is discussed here. The treatment of quantum electrodynamics is done from a canonical quantization viewpoint, and the discussion of electrons and positrons is now legendary.
Rating:
Summary: Highly (over)rated ?
Review: This is not a review as such, I just want to say I completely agree with the reader from Israel. Although a "classic" in the historical sense, I think the legendary status of this book much overdone. Nowadays there are MANY better QM texts out there from any angle and at any level.
Rating:
Summary: Read it to understand Dirac, but only AFTER you know QM
Review: This is NOT the book to read in order to study QM. But I think there are very good insights into how Dirac constructed the formulation that has become excepted. Also, you WILL find here a few things not available elsewhere, for example:
General physical priciples that lead you to the form of the equation of motion, and then Dirac tells the truth: that you now ASSUME that that thing in the equation is the energy, becuase it seems right (on acount of this and that). Also, why do we assume the commutation relation XP-PX=ih/(2*pi) ?
WHAT has lead the physicists to contruct this vector-space - linear-operators scheme?
Fundamentals like these can be found here, but rarely (I don't know any in fact, but maybe there are) in other texts. YOU CAN GET along with QM without this book, but it does have the true answers to some deep theoretical questions, if you ever wondered why the theory is formulated the way it is.
|
