Research in physics, conducted at the end of the 19th
century and in the first half of the 20th century, revealed exceptionally
peculiar nature of the laws governing the behaviour of microparticles –
atoms, electrons, and so on. On the basis of this research a new physical
theory called The growth of quantum mechanics turned out to be quite complicated and
prolonged. The mathematical part of the theory, and the rules linking the
theory with experiment, were constructed relatively quickly (by the beginning
of the thirties). However, the understanding of the physical and philosophical
substance of the mathematical symbols used in the theory was unresolved for
decades. In Fock's words, Many difficulties are involved in a mathematical interpretation of the
quantum-mechanical apparatus. These are associated with the dialectics of the
new laws, the radical revision of the very nature of the questions which
a physicist "is entitled to put to nature", the reinterpretation of the role of
the observer It is also not surprising that even today anyone who starts studying quantum mechanics encounters some sort of psychological barrier. This is not because of the mathematical complexity. The difficulty arises from the fact that it is difficult to break away from accepted concepts and to reorganize one's pattern of thinking which is based on everyday experience. Before starting a study of quantum mechanics, it is worthwhile getting an idea about its place and role in physics. We shall consider (naturally in the most general terms) the following three questions: What is quantum mechanics? What is the relation between classical physics and quantum mechanics? What specialists need quantum mechanics? So, what is quantum mechanics? The question can be answered in different ways. First and foremost,
quantum mechanics is a theory describing the properties of matter at the
level of From a broader point of view quantum mechanics should be treated
as the theoretical foundation of the modern theory of the structure and
properties of matter. In comparison with classical physics, quantum
mechanics considers the properties of matter What is the relation of quantum mechanics to classical physics? First of all quantum mechanics includes classical mechanics as a limiting (extreme) case. Upon a transition from microparticles to macroscopic bodies, quantum-mechanical laws are converted into the laws of classical mechanics. Because of this it is often stated, though not very accurately, that quantum mechanics "works" in the microworld and the classical mechanics, in the macroworld. This statement assumes the existence of an isolated "microworld" and an isolated "macroworld". In actual practice we can only speak of microparticles (microphenomena) and macroscopic bodies (macrophenomena). It is also significant that microphenomena form the basis of macrophenomena and that macroscopic bodies are made up of microparticles. Consequently, the transition from classical physics to quantum mechanics is a transition not from one "world" to another, but from a shallower to a deeper level of studying matter. This means that in studying the behaviour of microparticles, quantum mechanics considers in fact the same macro-particles, but on a more fundamental level. Besides, it must be remembered that the boundary between micro- and macrophenomena in general is quite conditional and flexible. Classical concepts are frequently found useful when considering microphenomena, while quantum-mechanical ideas help in the understanding of macrophenomena. There is even a special term "quantum macrophysics" which is applied, in particular, to quantum electronics, to the phenomena of superfluidity and superconductivity and to a number of other cases. In answering the question as to what specialists need quantum mechanics, we
mention beforehand that we have in mind specialists training in engineering
colleges. There are at least three branches of engineering for which a study of
quantum mechanics is absolutely essential. Firstly, there is the field of
The The
The author wishes to express his deep gratitude to Prof. I.I.Gurevich, Corresponding Member of the USSR Academy of Sciences, for the stimulating discussions which formed the basis of this book. Prof. Gurevich discussed the plan of the book and its preliminary drafts, and was kind enough to go through the manuscript. His advice not only helped mould the structure of the book, but also helped in the nature of exposition of the material. The subsection "The Essence of Quantum Mechanics" in Sec.16 is a direct
consequence of Prof. Gurevich's ideas. The author would like to record the deep
impression left on him by the works on quantum mechanics by the leading
American physicist R.Feynman. While reading the sections in
this book dealing with the applications of the idea of probability amplitude,
superposition principle, microparticles with two basic states, the reader can
easily detect a definite similarity in approach with the corresponding parts in
Feynman's "Lectures in Physics". The author was considerably influenced by
N.Bohr (in particular by his wonderful essays The author is especially indebted to Prof. M.I.Podgoretsky, D.Sc, for a thorough and extremely useful analysis of the manuscript. He is also grateful to Prof. Yu.A.Vdovin, Prof. E.E.Lovetsky, Prof. G.F.Drukarev, Prof. V.A.Dyakov, Prof. Yu.N.Pchelnikov, and Dr. A.M.Polyakov, all of whom took the trouble of going through the manuscript and made a number of valuable comments. Lastly, the author is indebted to his wife Aldina Tarasova for her constant interest in the writing of the book and her help in the preparation of the manuscript. But for her efforts, it would have been impossible to bring the book to its present form.
He who would study organic existence,First drives out the soul with rigid persistence, Then the parts in his hands he may hold and class But the spiritual link is lost, alas! Goethe ( Faust)
While talking about
Thus, if we know the position and velocity of a freely falling stone at a certain instant, we can precisely tell its position and velocity at any other instant, for example, at the instant when it hits the ground.
Next, let us try to apply the "principle of analysis" to an investigation of the structure of matter. We shall, in an imaginary way, break the object into smaller and smaller fractions, thus arriving finally at the molecules constituting the object. A further "breaking-up" leads us to the conclusion that molecules are made up of atoms. We then find out that atoms are made up of a nucleus and electrons. Accustomed to the tendency of splitting, we would like to know what an electron is made of. Even if we were able to get an answer to this question, we would have obviously asked next: What are the constituents, which form an electron, made of? And so on. We tend to accept the fact that such a "chain" of questions is endless. The same common sense will revolt against such a chain even though it is a direct consequence of classical thinking. Attempts were made at different times to solve the problem of this chain. We shall give two examples here. The first one is based on Plato's views on the structure of matter. He assumed that matter is made up of four "elements" – earth, water, air and fire. Each of these elements is in turn made of atoms having definite geometrical forms. The atoms of earth are cubic, those of water are icosahedral, while the atoms of air and fire are octahedral and tetrahedral, respectively. Finally, each atom was reduced to triangles. To Plato, a triangle appeared as the simplest and most perfect mathematical form, hence it cannot be made up of any constituents. In this way, Plato reduced the chain to the purely mathematical concept of a triangle and terminated it at this point. The other example is characteristic for the beginning of the 20th century. It makes use of the external similarity of form between the planetary model of the atom and the solar system. It is assumed that our solar system is nothing but an isolated atom of some other, gigantic world, and an ordinary atom is a sort of "solar system" for some third dwarfish world for which "our electron" is like a planet. In this case we admit the existence of an infinite row of more and more dwarfish worlds, just like more and more gigantic worlds. In such a system the structure of matter is described in accordance with the primitive "chinese box" principle. The "chinese box" principle of hollow tubes, according to which nature has a more or less similar structure, was not accepted by all the physicists of older generations. However, this principle is quite characteristic of classical physics, it conforms to classical concepts, and follows directly from the classical principle of analysis. In this connection, criticizing Pascal's views that the smallest and the largest objects have the same structure, Langevin pointed out that this would lead to the same aspects of reality being revealed at all levels. The universe should then be reflected in an absolutely identical fashion in all objects, though on a much smaller scale. Fortunately, reality turns out to be much more diverse and interesting. Thus, we are convinced that a successive application of the principles of classical physics may, in some cases, lead to results which appear doubtful. This indicates the existence of situations for which classical principles are not applicable. Thus it is to be expected that for a sufficiently strong "breaking-up" of matter, the principle of analysis must become redundant (thus the idea of the independence of the object of measurement from the measuring instrument must also become obsolete). In this context the question "what is an electron made of?" would simply appear to have lost its meaning. If this is so, we must accept the Lev Vasilievich TARASOV
The author was born in 1934 and graduated from Moscow Engineering Physics Institute in 1958 specializing in the field of theoretical nuclear physics. He was awarded his PhD in Mathematics and Physics in 1968, was appointed Associate Professor in 1969, and Professor in 1983. From 1989 to 1992 he was Head of the Department of the Methodology for Natural Sciences Teaching at the Moscow Institute for the Advanced Training for Teachers. Between 1992 and 1998 he was Head of the Department of Physics at Moscow State Pedagogical Open University. In 1994 he was awarded the medal "For Excellence in Public Education" for
developing a new model of comprehensive school |