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The Principles of Quantum Mechanics Paperback – January 8, 2013
"Devoted" by Dean Koontz
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- Item Weight : 1.16 pounds
- Paperback : 330 pages
- ISBN-10 : 1607965607
- ISBN-13 : 978-1607965602
- Product Dimensions : 6.69 x 0.69 x 9.61 inches
- Publisher : www.snowballpublishing.com (January 8, 2013)
- Language: : English
- Customer Reviews:
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Theory. Furthermore, one of the best "popularized" books on Quantum Mechanics
is the pocket sized "The Quantum World" which follows the topics in Dirac's "Quantum
Mechanics" for laymen by Professor of Mathematical Physics, at Cambridge, J. C.
Polkinghorne. He learned the subject attending PAM Dirac's classes from his own book.
Professor PAM Dirac ended his days by retiring to a Professor Emeritus chair at Florida
State University (right here) in Tallahassee, FL.
The discovery of the positron is illustrated clearly, later to be confirmed experimentally by Carl Anderson and leading to the 1933 Nobel for Dirac (shared with Schrödinger).
Books like this, despite their age, are worth keeping in one’s library, as is John von Neumann’s Mathematical Foundation of Quantum Mechanics (also from the early 1930s, but timeless in its value).
He wrote in the Preface to the First Edition (1930) of this book, “The classical tradition … led to a physics whose aim was to make assumptions about the mechanism and forces connecting these observable objects, to account for their behavior in the simplest possible way. It has become increasingly evident in recent times, however, that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies. The formulation of these laws requires the use of the mathematics of transformations… From the mathematical side the approach to the new theories presents no difficulties… For this reason a book on the new physics… must be essentially mathematical… In this book I have tried to keep the physics to the forefront, by beginning with an entirely physical chapter and in the later work examining the physical meaning underlying the formalism wherever possible.”
He explains, “Causality applies only to a system which is left undisturbed. If a system is small, we cannot observe it without producing a serious disturbance and hence we cannot expect to find any causal connection between the results of our observations. Causality will still be assumed to apply to undisturbed systems and the equations which will be set up to described an undisturbed system will be differential equations expressing a causal connection between conditions at one time and conditions at a later time… There is an unavoidable indeterminacy in the calculation of observational results, the theory enabling us to calculate in general only the probability of our obtaining a particular result when we make an observation.” (Pg. 4)
He notes, “quantum mechanics is able to effect a reconciliation of the wave and corpuscular properties of light. The essential point is the association of each of the transactional states of a photon with one of the wave functions of ordinary wave optics. The nature of this association cannot be pictured on a basis of classical mechanics, but is something entirely new… The association can be interpreted only statistically, the wave function giving us information about the probability of our finding the photon in any particular place when we make an observation of where it is.” (Pg. 9)
He states, “The general principle of superposition of quantum mechanics … requires us to assume that between these states there exist peculiar relationships such that whenever the system is definitely in one state we can consider it as being partly in each of two or more states.. The original state must be regarded as the result of a kind of superposition of the two or more new states, in a way that cannot be resolved on classical ideas… The nature of the relationships which the superposition principle requires to exist between the states of any system is of a kind that cannot be explained in terms of familiar physical concepts… There is a entirely new idea involved, to which one must get accustomed and in terms of which one must proceed to build up any exact mathematical theory, without having any detailed classical picture.” (Pg. 12)
He observes, “Most quantum problems … cannot be solved exactly with the present resources of mathematics, as they lead to equations whose solutions cannot be expressed in finite terms with the help of the ordinary functions of analysis… There are two distinct methods in perturbation theory. In one of these the perturbation is considered as causing a modification of the states of motion of the unperturbed system. In the other w do not consider any modification to be made in the states of the unperturbed system, but we suppose that the perturbed system, instead of remaining permanently in ONE of these states, is continually changing from one to another, or making transitions, under the influence of the perturbation. Which method is to be used in any particular case depends on the nature of the problem to be solved.” (Pg. 167)
He says, “we shall investigate problems connected with a particle which, coming from infinity, encounters or ‘collides with’ some atomic system and, after being scattered through a certain angle, goes off to infinity again. The atomic system which does the scattering we shall call … the ‘scatterer.’ … The scatterer is usually assumed to be of infinite mass and to be at rest throughout the scattering process… We must take into account the possibility that the scatterer, considered as a system by itself, may have a number of different stationary states and that if it is initially in one of these states when the particle arrives from infinity, it may be left in a different one when the particle goes off to infinity again. The colliding particle may this induce transitions in the scatterer.” (Pg. 185)
He points out, “If a system in atomic physic contains a number of particles of the same kind, e.g., a number of electrons, the particles are absolutely indistinguishable one from another. No observable change is made when two of them are interchanged. This circumstance gives rise to some curious phenomena in quantum mechanics having no analogue in classical theory, which arise from the fact that in quantum mechanics a transition may occur resulting in merely the interchange of two similar particles, which transition then could not be detected by any observational means.” (Pg. 207)
He concludes, “Quantum mechanics may be defined as the application of equations of motion to atomic particles… The domain of the applicability of the theory is mainly the treatment of electrons and other charged particles interacting with the electromagnetic field---a domain which now includes most of low-energy physics and chemistry. Now there are other kinds of interactions, which are revealed in high-energy physics and are important for the description of atomic nuclei. These interactions are not at present sufficiently well understood to be incorporated into a system of equations of motion… It is to be hoped that with increasing knowledge a way will eventually 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.” (Pg. 312)
This book will be “must reading” for those seriously studying the development of contemporary physics.
However, the introduction contains some salient points on the introduction of quantum theory via the phenomenon of polarization that is most memorable. In fact it stood as a revolution in my thinking of quantum theory. Then we move onto the Poisson Brackets and his derivation involving the commutator. Now as to why he choose the Poisson Brackets, that is still a bit of a mystery, but at least he derived the relationship in full as opposed to almost every quantum text I have seen (too many to count), with the exception of Kai Lam's. So for mathematical completeness, this is about the most complete quantum text I have seen, though I will be examining Steeb's soon, which looks nice.
The part that got me bored was when we get to the section on Angular Momentum. It felt like he got out of breath at that point, and just started writing mechanically. The first basic parts were so inspired, I think he could have just published that as the introduction, and left the rest for a more advanced part he could have worked on well late into his life. But it feels like he rushed to put that last portion in, which was clearly not as well understood as the rest, especially the portion on spin. I think his own equation, the Dirac equation, mystified him as did spin, and still does to many physicists today. However deriving the structure of quantum theory and the operators, it is clear to me that he understood that better than just about every physicist, next to Max Born. Born simply lacked the sophistication of a mathematician to keep up with Dirac.
So this book stands as a historical edifice in quantum theory, next to Max Born's Atomic Physics. They are both foundational and helped me move forward greatly in my understanding of quantum theory. However it is clear that more texts will be continued to come out for the future generations as we understand this precious subject more and more. However I can say that up to right now, these two texts are the best you can buy, and then there is also Pauli's books on the subject, and then like I said Steeb may be of interest, but my review for that will await.
Top reviews from other countries
Dirac's Principles remain, to this day, a vital tool in the understanding of mechanics.
Das Buch kommt ohne jede Grafik oder erläuternde Illustrationen aus und es scheint, als habe man eine ältere 4. Auflage abgescannt und hier neu abgedruckt. Der Text ist keinesfalls neu gesetzt worden, was der Lesbarkeit, gerade der Formelausdrücke, aber nicht schadet.
Einen Stern Abzug gibt es für die Wahl des mangelhaften Papiers. Bei der Hervorhebung wichtiger Stellen mit Textmarker schlägt dessen Tinte durch, so dass man ungewollt auch die Rückseite mitmarkiert, was keinen Sinn macht und beim schnellen Nachschlagen erheblich nervt.
Bei entsprechenden Vorkenntnissen sehr zum Selbststudium geeignet.
É claro que o "fácil" escrito acima deve ser visto dentro de um certo contexto. O leitor deve se sentir confortável com Álgebra Linear e Cálculo básico. Por outro lado este é um conhecimento de primeiro ano de graduação em qualquer curso de STEM.
Além disso, é importante que o leitor sinta-se mais confortável em um ambiente "algébrico" do que "geométrico". O livro é famoso por não conter nenhum diagrama.
Dito isso, recomendo a leitura para qualquer pessoa interessada em conhecer Mecânica Quântica a partir de princípios básicos os quais são simples de entender e aplicar (aceita-los é outra história...).
Lo consiglio assolutamene a chi vuole comprendere le basi epistemologiche della teoria