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Introduction to Modern Physics [UNIT III. STATISTICAL MECHANICS]

Renu Singh

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

The standard undergraduate programme in physics of all Indian Universities includes courses on Special Theory of Relativity, Quantum Mechanics, Statistical Mechanics, Atomic and Molecular Spectroscopy, Solid State Physics, Semiconductor Physics and Nuclear Physics. To provide study material on such diverse topics is obviously a difficult task partly because of the huge amount of material and partly because of the different nature of concepts used in these branches of physics. This book comprises of self-contained study materials on Special Theory of Relativity, Quantum Mechanics, Statistical Mechanics, Atomic and Molecular Spectroscopy. In this book the author has made a modest attempt to provide standard material to undergraduate students at one place. The author realizes that the way he has presented and explained the subject matter is not the only way; possibilities of better presentation and the way of better explanation of intrigue concepts are always there. The author has been very careful in selecting the topics, laying their sequence and the style of presentation so that student may not be afraid of learning new concepts. Realizing the mental state of undergraduate students, every attempt has been made to present the material in most elementary and digestible form. The author feels that he cannot guess as to how far he has come up in his endeavour and to the expectations of esteemed readers. They have to judge his work critically and pass their constructive criticism either to him or to the publishers so that they can be incorporated in further editions. To err is human. The author will be glad to receive comments on conceptual mistakes and misinterpretation if any that have escaped his attention. A sufficiently large number of solved examples have been added at appropriate places to make the readers feel confident in applying the basic principles.

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The standard undergraduate programme in physics of all Indian Universities includes courses on
Special Theory of Relativity, Quantum Mechanics, Statistical Mechanics, Atomic and Molecular
Spectroscopy, Solid State Physics, Semiconductor Physics and Nuclear Physics. To provide study material
on such diverse topics is obviously a difficult task partly because of the huge amount of material and
partly because of the different nature of concepts used in these branches of physics. This book comprises
of self-contained study materials on Special Theory of Relativity, Quantum Mechanics, Statistical
Mechanics, Atomic and Molecular Spectroscopy. In this book the author has made a modest attempt to
provide standard material to undergraduate students at one place. The author realizes that the way he
has presented and explained the subject matter is not the only way; possibilities of better presentation
and the way of better explanation of intrigue concepts are always there. The author has been very
careful in selecting the topics, laying their sequence and the style of presentation so that student may
not be afraid of learning new concepts. Realizing the mental state of undergraduate students, every
attempt has been made to present the material in most elementary and digestible form. The author feels
that he cannot guess as to how far he has come up in his endeavour and to the expectations of
esteemed readers. They have to judge his work critically and pass their constructive criticism either to
him or to the publishers so that they can be incorporated in further editions. To err is human. The
author will be glad to receive comments on conceptual mistakes and misinterpretation if any that have
escaped his attention.
A sufficiently large number of solved examples have been added at appropriate places to make the
readers feel confident in applying the basic principles.
The book is designed to serve as an `upper-level one-semester course in Quantum mechanics for students majoring in physics or related topics'. To that purpose the author has organised the contents into roughly six parts, giving first a historical introduction into quanta and matter waves, then the solution of the Schrödinger equations in one, and subsequently in three dimensions; in a fourth part spin and the concept of identical particles are explained, whilst in the next the approximation (perturbation) methods and their application to atomic systems and the creation and transfer of radiations. Finally there are two chapters on molecular and solid state physics. Each chapter is accompanied by a selection of appropriate problems. Appendix, index plus diskette are provided. As the author states, the topics and examples were taken from his other (successful) book, Introduction to Modern Physics . It appears to the reviewer that the present account may indeed serve as a first introduction into the elementary aspects of quantum mechanics, with particular emphasis on explaining the basic concepts (like spin, statistics, even the Einstein-Podolsky-Rosen paradox). Addressed are the slightly advanced students of science. The language is clear, the formal apparatus does not overwhelm the reader, and the figures have been carefully selected and drawn. We do recommend the book for the purpose envisaged. It raises the appetite for a more systematic and extended study of the subject.
After a short review of some essential concepts of classical physics (with a discussion of the so-called `scientific method', which is rarely found in textbooks of this kind), including the classical description of particles and waves, together with a sketch of statistical thermodynamics, the basics of quantum mechanics are introduced. The third chapter then treats systems of identical particles and their statistics, as well as the statistics of discrete energy levels. This is followed by an extensive presentation of the behaviour of quantum particles in periodic potentials with obvious applications to crystalline materials, including metals, insulators, semiconductors and superconductors. The band structure of some special materials, intrinsic carrier concentrations and electrons in metals are further topics of this main chapter. In most quantum mechanics textbooks the subjects of the fifth chapter, quantum wells, harmonic oscillators and the hydrogen atom, are usually introduced before a discussion of periodic potentials, but the author's exposition makes it quite plausible to place them afterwards. The concept of tunnelling through potential barriers and important application examples, ranging from ohmic contacts to scanning tunnelling microscopy and even radioactivity, make up the next chapter. Some approximation methods, i.e. stationary perturbation theory with applications to coupled wells, and the variational method, are treated in the next chapter. The final chapter dealing with quantum mechanics then is concerned with scattering and collision problems, again, of course, with examples from solid state physics. This last chapter, however, looks somehow merely added on, since it introduces only quite briefly the theory of special relativity -almost certainly in order not to leave out this important revolution of modern physics. Three appendices, on Fermi's Golden Rule, Boltzmann's transport theory and quantum interference devices, round off the contents. The book abounds with links to modern technologies that have evolved out of quantum mechanics (with, of course, the exception of the last chapter on special relativity). To the reviewer this constitutes its outstanding value as a textbook on quantum mechanics for engineering students. In addition, about 100 solved numerical examples in the text illustrate very lucidly some of the more abstract concepts, and at the end of the chapters altogether 200 further problems are posed. Although some of the concepts and results of quantum mechanics are introduced in a seemingly ad hoc manner, nevertheless the book as a whole certainly represents a valuable teaching tool at engineering schools; even physics majors may profit from the wealth of technical applications not usually found in their textbooks on quantum mechanics.
This concise and accessible book provides a detailed introduction to the fundamental principles of atomic physics at an undergraduate level. Concepts are explained in an intuitive way and the book assumes only a basic knowledge of quantum mechanics and electromagnetism. With a compact format specifically designed for students, the first part of the book covers the key principles of the subject, including the quantum theory of the hydrogen atom, radiative transitions, the shell model of multi-electron atoms, spin-orbit coupling, and the effects of external fields. The second part provides an introduction to the four key applications of atomic physics: lasers, cold atoms, solid-state spectroscopy and astrophysics. This highly pedagogical text includes worked examples and end of chapter problems to allow students to test their knowledge, as well as numerous diagrams of key concepts, making it perfect for undergraduate students looking for a succinct primer on the concepts and applications of atomic physics.
Abstract This book provides the reader with a contemporary and comprehensive introduction to Quantum Mechanics. It is suitable for beginners as well as for more advanced university students. Quantum mechanics is presented in a pedagogical fashion, with a clear logical organization. The various concepts and methods are introduced first in elementary terms, and later developed into more precise formulations. Systematic studies of approximation methods and the discussion of a wide class of physical applications follow. Part I of the book, together with the opening sections of Part II, provide adequate material for an introductory course of one semester at most universities. The rest of the book might be used in an advanced course on Quantum Mechanics. The basic material is fairly standard, even though some discussions such as those on general systems with time-dependent Hamiltonians, on metastable systems, as well as the discussions in some of the Complement sections, may not be found in other textbooks. The book also contains many original observations or new ways of illustrating even well-known subjects. In fact, the authors wish to convey in this book the sense of wonder in the logical simplicity and at the same time the beauty of subtle and far-reaching consequences of Quantum Mechanics, to young physics students in particular. Problem sets are provided at the end of each chapter, to be solved either analytically or by numerical methods. The solutions to both types of problems are given as separate pdf files or as Mathematica notebooks (there are 88 of them), all together on a CD accompanying the textbook. The presence of such a collection of numerical analyses enriches the main text and is one of the characteristic features of the book. With the many interesting systems discussed, the book will also be a useful reference for researchers and teachers. It provides the reader with a unique, enjoyable and rather complete textbook of Quantum Mechanics, destined to set a new standard for many years to come.
This concise and accessible book provides a detailed introduction to the fundamental principles of atomic physics at an undergraduate level. Concepts are explained in an intuitive way and the book assumes only a basic knowledge of quantum mechanics and electromagnetism. With a compact format specifically designed for students, the first part of the book covers the key principles of the subject, including the quantum theory of the hydrogen atom, radiative transitions, the shell model of multi-electron atoms, spin-orbit coupling, and the effects of external fields. The second part provides an introduction to the four key applications of atomic physics: lasers, cold atoms, solid-state spectroscopy and astrophysics. This highly pedagogical text includes worked examples and end of chapter problems to allow students to test their knowledge, as well as numerous diagrams of key concepts, making it perfect for undergraduate students looking for a succinct primer on the concepts and applications of atomic physics.
This book is particularly designed for the undergraduate and post graduate level students, specially beginners of quantum mechanics, of Indian as well as foreign universities.The book begins with a firm grounding in the basics of quantum mechanics.Special effort is given to emphasize things by providing sufficient numerical exposure to the students. Rich selection of problems and their simple solutions in every chapter, is bound to give the students a firm grip on the topic. Apart from those, formulas for numerical problems are highlighted properly to help the students to select them efficiently whenever necessary. In between every chapter, a large number of unsolved problems with due hints are given so that the readers can apply the underlying principles in solving these problems.Conceived mainly for graduate/post graduate students, this book will also be helpful for all, who wish to acquire some knowledge of quantum mechanics.