This book is based on a series of lectures delivered by the authors at the Moscow State University over many years. It provides a systematic analysis of the theoretical concepts of quantum mechanics and some of its applications.
Quantum mechanics, whose basic laws were formulated between the years 1925 and 1928, is one of the most Important branches of modern theoretical physics. It investigates the behaviour of electrons and other microparticles in atoms, molecules, solids, as well as in external electromagnetic fields.
The development of quantum mechanics took place in several stages.
The first stage is associated with the accumulation of experimental facts concerning thermal electromagnetic radiation, photoelectric effect, the Compton effect, etc. These facts were not compatible with classical electrodynamics, and in order to explain them it was postulated that besides having a wavelike nature, light must also have corpuscular properties. This assumption was used in the quantum theory of Planck and Einstein.
Rutherford's experiments on the scattering of alpha-particles in matter formed the basis of Bohr's semiclassical theory of an atom. This marked the beginning of the second stage in the development of quantum mechanics.
Finally, the third stage began with the observation of a number.of experimental facts (diffraction and interference of electron beams) which were associated with the corpuscular and wave properties of electrons. Schrodinger's equation (1926), which was an extension of the de Broglie hypothesis on electron waves, was the first general result taking into account the wave properties of microparticles. Earlier, in 1925, the quantum theory of atom was formulated by Heisenberg in the form of matrix mechanics. Thus, while in the classical theory light was treated as a wave and electron was considered as a particle, this distinction was removed in quantum mechanics and it was accepted that light and electrons may exhibit corpuscular as well as wave properties under appropriate conditions. This is called the wave-particle duality.
This book has been divided into three parts. The first part describes the nonrelativistic Schrodinger theory, while the second part deals with Dirac's relativistic theory. Finally, the third part is devoted to the many-particle theory.
The emphasis in the first two parts of the book has been laid on the basic concepts of quantum mechanics, which have been illustrated with the help of characteristic examples. The authors have endeavoured to acquaint the reader with the physical aspects of the theory as well as with the mathematical apparatus associated with it. Since the book mainly comprises a graduate course material on quantum mechanics, several special problems have been included in the text. Thus, while describing the theory of a hydrogen-like atom, different curvilinear orthogonal coordinates have been considered; creation and annihilation operators have been introduced in the harmonic oscillator theory; the method of Regge's complex poles has been described in the scattering theory, and so on. The application of the representation theory in quantum mechanics has also been demonstrated by taking the example of a harmonic oscillator. Besides, the basic principles of second quantization have also been included in this book. A knowledge of these principles is essential for understanding the modern theory of radiation. The second quantization has been considered both for an electromagnetic field and the Dirac electron field.
The third part of the book deals with the many-particle theory, and, in particular, the structure of many-electron atoms and simple molecules. Separate sections have been devoted to a description of the fundamentals of the solid state theory. As and where necessary, we have briefly touched upon some modern problems in the theory of solids, for example superconductivity and other related effects. The last section describes the theory of motion- and radiation of the relativistic electron in a constant and uniform magnetic field (synchrotron radiation).
The material presented in this book is intended for undergraduate students studying for a-physics degree. It can be also used by students of such institutes where the basic concepts of quantum mechanics are taught.
The authors are grateful to Yu. M. Loskutov, D. V. Gal'tsov, A. V. Borisov, and M. M. Kolesnikov for their help in preparing the manuscript. They made several significant comments and helped