An approach to the teaching of the chapter ’’Equivalent particles and the exclusion principle’’ (which is part of an undergraduate quantum mechanics course) is outlined. The clarification of basic concepts and the preventive treatment of anticipated beginners’ misunderstandings are emphasized. The exclusion principle is taught by confronting it with the principle of the ’’identity of the indiscernible’’ of Leibnitz. The limits of the analogy between general ideas belonging to different disciplines are outlined by discussing the inability of philosophy to predict the directions in which the physical theory actually advances.
An approach to the teaching of the chapter ’’Equivalent particles and the exclusion principle’’ (which is part of an undergraduate quantum mechanics course) is outlined. The clarification of basic concepts and the preventive treatment of anticipated beginners’ misunderstandings are emphasized. The exclusion principle is taught by confronting it with the principle of the ’’identity of the indiscernible’’ of Leibnitz. The limits of the analogy between general ideas belonging to different disciplines are outlined by discussing the inability of philosophy to predict the directions in which the physical theory actually advances.
The textbook covers the background theory of various effects discussed from first principles, as clearly as possible, to introduce students to the main ideas of quantum physics and to teach the basic mathematical methods and techniques used in the fields of advanced quantum physics, atomic physics, laser physics, nanotechnology, quantum chemistry, and theoretical mathematics. Many of the predictions of quantum physics appear to be contrary to our intuitive perceptions, and the student will learn how it comes about that microscopic objects (particles) behave in unusual ways that are called quantum effects, what we mean by quantum, and where this idea came from. The textbook is supplemented with Problems and Solutions in Quantum Physics, which contains a wide range of tutorial problems from simple confidence builders to fairly challenging problems that provide adequate understanding of the basic concepts of quantum physics.
This book is based on notes from the course developed and taught for more than 30 years at the Department of Mathematics of Leningrad University. The goal of the course was to present the basics of quantum mechanics and its mathematical content to students in mathematics. This book differs from the majority of other textbooks on the subject in that much more attention is paid to general principles of quantum mechanics. In particular, the authors describe in detail the relation between classical and quantum mechanics. When selecting particular topics, the authors emphasize those that are related to interesting mathematical theories. In particular, the book contains a discussion of problems related to group representation theory and to scattering theory. This book is rather elementary and concise, and it does not require prerequisites beyond the standard undergraduate mathematical curriculum. It is aimed at giving a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.
[I] think I can safely say that nobody understands quantum mechanics. Richard Feynman, The Character of Physical Law Quantum mechanics [is] that mysterious, confusing discipline, which none of us really understands but which we know how to use. It works perfectly, as far as we can tell, in describing physical reality, but it is a ‘counter-intuitive discipline’… Murray Gell-Mann, Questions for the Future [The quantum] postulate implies a renunciation as regards the causal space-time co-ordination of atomic processes. Niels Bohr, Atomic Theory and the Description of Nature It should be emphasized, however, that the probability function does not in itself represent a course of events in the course of time. It represents a tendency for events and our knowledge of events. The probability function can be connected with reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system. [T]he idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them…is impossible … Werner Heisenberg, Physics and Philosophy [In] quantum theory it is the principle of causality , or more accurately that of determinism , which must be dropped and replaced by something else.… We now have a new form of the law of causality.… It is as follows: if in a certain process the initial conditions are determined as accurately as the uncertainty relations permit, then the probabilities of all possible subsequent states are governed by exact laws. Max Born, The Restless Universe
Scope of this book Quantum mechanics is a difficult subject, and this book is intended to help the reader overcome the main difficulties in the way to understanding it. The first part of the book, Chs. 2–16, contains a systematic presentation of the basic principles of quantum theory, along with a number of examples which illustrate how these principles apply to particular quantum systems. The applications are, for the most part, limited to toy models whose simple structure allows one to see what is going on without using complicated mathematics or lengthy formulas. The principles themselves, however, are formulated in such a way that they can be applied to (almost) any nonrelativistic quantum system. In the second part of the book, Chs. 17–25, these principles are applied to quantum measurements and various quantum paradoxes, subjects which give rise to serious conceptual problems when they are not treated in a fully consistent manner. The final chapters are of a somewhat different character. Chapter 26 on decoherence and the classical limit of quantum theory is a very sketchy introduction to these important topics along with some indication as to how the basic principles presented in the first part of the book can be used for understanding them. Chapter 27 on quantum theory and reality belongs to the interface between physics and philosophy and indicates why quantum theory is compatible with a real world whose existence is not dependent on what scientists think and believe, or the experiments they choose to carry out. The Bibliography contains references for those interested in further reading or in tracing the origin of some of the ideas presented in earlier chapters.
There are several (general) philosophy of physics textbooks on the market.1 An
obvious question to ask at the outset then is: Why another one? In his “Some
Philosophical Aspects of Particle Physics”, Michael Redhead bemoans the common practice of philosophers of science of dealing with examples “which are no
longer of current research interest in science” ((1980), p. 279). This practice is
still common even among many philosophers of physics, and, for the most part,
the available textbooks continue to engage in this practice. Generally, one finds a
little spacetime, a little statistical mechanics, and a little quantum theory. Now,
these are of course the ‘pillars’ of modern physics, so it is what we should expect
to be covered in any textbook on the philosophy of physics worth its salt (and,
indeed, they are well represented in this book). However, the issues that are
dealt with are usually very old fashioned and very limited in scope: ‘spacetime’
means ‘the twins paradox’ (and possibly conventionalism); ‘statistical mechanics’
means ‘time asymmetry’; and ‘quantum theory’ means ‘the measurement problem’. Redhead is surely right that this leads physicists to “regard philosophy of
science as somewhat irrelevant”. Rightly so, too, if this were in fact representative of much of what actually goes on in philosophy of physics. However, the
state of play as represented in philosophy of physics and (some) philosophy of
science journals shows a very different level of engagement, with philosophers
of physics investigating the frontiers of scientific research. This disparity (or the
impression of such) is the raison d’eˆtre for the book you are now reading. The result is an introductory textbook covering those portions of philosophy of physics
research that other textbooks fail to cover, or cover only very briefly or very
simplistically. The three pillars of modern physics-relativity, quantum theory
and statistical mechanics-are still represented, then, but from a more advanced
and contemporary perspective.