Norman H. March – författare

The theory of the inhomogeneous electron gas had its origin in the Thomas­ Fermi statistical theory, which is discussed in the first chapter of this book. This already leads to significant physical results for the binding energies of atomic ions, though because it leaves out shell structure the results of such a theory cannot reflect the richness of the Periodic Table. Therefore, for a long time, the earlier method proposed by Hartree, in which each electron is assigned its own personal wave function and energy, dominated atomic theory. The extension of the Hartree theory by Fock, to include exchange, had its parallel in the density description when Dirac showed how to incorporate exchange in the Thomas-Fermi theory. Considerably later, in 1951, Slater, in an important paper, showed how a result similar to but not identical with that of Dirac followed as a simplification of the Hartree-Fock method. It was Gombas and other workers who recognized that one could also incorporate electron correlation consistently into the Thomas-Fermi-Dirac theory by using uniform electron gas relations locally, and progress had been made along all these avenues by the 1950s.

This book has its origins in the 1982 Spring College held at the Interna­ tional Centre for Theoretical Physics, Miramare, Trieste. The primary aim is to give a broad coverage of liquids and amorphous solids, at a level suitable for graduate students and research workers in condensed-matter physics, physical chemistry, and materials science. The book is intended for experimental workers with interests in the basic theory. While the topics covered are many, it was planned to place special emphasis on both static structure and dynamics, including electronic transport. This emphasis is evident from the rather complete coverage of the determination of static structure from both diffraction experiments and, for amorphous solids especially, from model building. The theory of the structure of liquids and liquid mixtures is then dealt with from the standpoint of, first, basic statistical mechanics and, subsequently, pair potentials constructed from the electron theory of simple metals and their alloys. The discussion of static structure is completed in two chapters with rather different emphases on liquid surfaces and interfaces. The first deals with the basic statistical mechanics of neutral and charged interfaces, while the second is concerned with solvation and double-layer effects. Dynamic structure is introduced by a comprehensive discussion of single-particle motion in liquids. This is followed by the structure and dynamics of charged fluids, where again much basic statistical mechanics is developed.

This book is concerned primarily with the fundamental theory underlying the physical and chemical properties of crystalIine semiconductors. After basic introductory material on chemical bonding, electronic band structure, phonons, and electronic transport, some emphasis is placed on surface and interfacial properties, as weil as effects of doping with a variety of impurities. Against this background, the use of such materials in device physics is examined and aspects of materials preparation are discussed briefty. The level of presentation is suitable for postgraduate students and research workers in solid-state physics and chemistry, materials science, and electrical and electronic engineering. Finally, it may be of interest to note that this book originated in a College organized at the International Centre for Theoretical Physics, Trieste, in Spring 1984. P. N. Butcher N. H. March M. P. Tosi vii Contents 1. Bonds and Bands in Semiconductors 1 E. Mooser 1. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 2. The Semiconducting Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 3. Bond Approach Versus Band Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 4. Construction of the Localized X by Linear Combination of n Atomic Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1. 5. The General Octet Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1. 6. The Aufbau-Principle of the Crystal Structure of Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1. 7. A Building Principle for Polyanionic Structures . . . . . . . . . . . . . . . . . . . . . . 29 I. H. Structural Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1. 9. Chemical Bonds and Semiconductivity in Transition-Element Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1. 10. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2. Electronic Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 G. Grosso 2. 1. Two Different Strategies for Band-Structure Calculations . . . . . . . 55 2. 2. The Tight-Binding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This volume is concerned with the theoretical description of patterns and instabilities and their relevance to physics, chemistry, and biology. More specifically, the theme of the work is the theory of nonlinear physical systems with emphasis on the mechanisms leading to the appearance of regular patterns of ordered behavior and chaotic patterns of stochastic behavior. The aim is to present basic concepts and current problems from a variety of points of view. In spite of the emphasis on concepts, some effort has been made to bring together experimental observations and theoretical mechanisms to provide a basic understanding of the aspects of the behavior of nonlinear systems which have a measure of generality. Chaos theory has become a real challenge to physicists with very different interests and also in many other disciplines, of which astronomy, chemistry, medicine, meteorology, economics, and social theory are already embraced at the time of writing. The study of chaos-related phenomena has a truly interdisciplinary charac­ ter and makes use of important concepts and methods from other disciplines. As one important example, for the description of chaotic structures the branch of mathematics called fractal geometry (associated particularly with the name of Mandelbrot) has proved invaluable. For the discussion of the richness of ordered structures which appear, one relies on the theory of pattern recognition. It is relevant to mention that, to date, computer studies have greatly aided the analysis of theoretical models describing chaos.

Presenting the latest advances in artificial structures, this volume discusses in-depth the structure and electron transport mechanisms of quantum wells, superlattices, quantum wires, and quantum dots. It will serve as an invaluable reference and review for researchers and graduate students in solid-state physics, materials science, and electrical and electronic engineering.

In this introductory chemical physics textbook, the authors discuss the interactions, bonding, electron density, and experimental techniques of free molecules, and apply spectroscopic methods to determine molecular parameters, dynamics, and chemical reactions.

This book had its origins in lectures presented at EPFL, Lausanne, during two separate visits (the most recent being to IRRMA). The author is most grateful to Professors A. Baldereschi, R. Car, and A. Quattropani for making these visits possible, and for the splendidly stimulating environment provided. Professors S. Baroni and R. Resta also influenced considerably the presentation of material by constructive help and comments. Most importantly, Chapters 4 and 5 were originally prepared for a review article by Professor G. Senatore, then at Pavia and now in Trieste, and myself for Reviews of Modem Physics (1994). In the 'course of this collaboration, he has taught me a great deal, especially about quantum Monte Carlo procedures, and Chapter 5 is based directly on this review article. Also in Chapter 4, my original draft on Gutzwiller's method has been transformed by his deeper understanding; again this is reflected directly in Chapter 4; especially in the earlier sections. In addition to the above background, it is relevant here to point out that, as a backcloth for the present, largely "state of the art," account, there are two highly relevant earlier books: The Many-body Problem in Quantum Mechanics with W.

The problem of molecules interacting with metal surfaces has for a very long time been recognized to be of considerable technological as well as fundamental importance. Thus in the former category, a substantial number of important synthetic reactions for industrial purposes make use of metal surfaces as catalysts. Or again, problems of corrosion of metals are of great practical importance, such as in nuclear-reactor technology [see, for instance, my earlier articles, in: Physics Bulletin, Volume 25, p. 582, Institute of Physics, UK (1974); and in: Physics and Contemporqry Needs (Riazuddin, ed. ), Vol. 1, p. 53, Plenum Press, New York (1977)]. It is therefore of significance to strive to gain a more fundamental understand­ ing of the atomic, and ultimately the electronic, processes that occur when a molecule is brought into the proximity of a metal surface. The present volume focuses mainly on the theory and concepts involved; however, it is intended for readers in chemistry, physics, and materials science who are not specialists in theory but nevertheless wish to learn more about this truly interdisciplinary area of theoretical science. The aim of the book is to present the way in which valence theory can be synthesized with the understanding of metals that has been gained over the last half century or so. While advanced theory has at times been necessary, is largely presented in an extensive set of Appendixes.

This book deals with three related areas having both fundamental and technological interest. In the first part, the objective is to provide a bird's­ eye view on structure in polymeric solids. This is then complemented by a chapter, directly technological in its emphasis, dealing with the influence of processing on polymeric materials. In spite of the technological interest, this leads to some of the current fundamental theory. Part II, concerned with liquid crystals, starts with a discussion of the physics of the various types of material, and concludes with a treatment of optical applications. Again, aspects of the theory are stressed though this part is basically phenomenological in character. In Part III, an account is given first of the use of chemical-bonding arguments in understanding the electronic structure of low-dimensional solids, followed by a comprehensive treatment of the influence of dimen­ sionality on phase transitions. A brief summary of dielectric screening in low-dimensional solids follows. Space-charge layers are then treated, including semiconductor inversion layers. Effects of limited dimensionality on superconductivity are also emphasized. Part IV concludes the volume with two specialized topics: electronic structure of biopolymers, and topological defects and disordered systems. The Editors wish to acknowledge that this book had its origins in the material presented at a course organized by the International Centre for Theoretical Physics, Trieste.

The problem of molecules interacting with metal surfaces has for a very long time been recognized to be of considerable technological as well as fundamental importance. Thus in the former category, a substantial number of important synthetic reactions for industrial purposes make use of metal surfaces as catalysts. Or again, problems of corrosion of metals are of great practical importance, such as in nuclear-reactor technology [see, for instance, my earlier articles, in: Physics Bulletin, Volume 25, p. 582, Institute of Physics, UK (1974); and in: Physics and Contemporqry Needs (Riazuddin, ed. ), Vol. 1, p. 53, Plenum Press, New York (1977)]. It is therefore of significance to strive to gain a more fundamental understand­ ing of the atomic, and ultimately the electronic, processes that occur when a molecule is brought into the proximity of a metal surface. The present volume focuses mainly on the theory and concepts involved; however, it is intended for readers in chemistry, physics, and materials science who are not specialists in theory but nevertheless wish to learn more about this truly interdisciplinary area of theoretical science. The aim of the book is to present the way in which valence theory can be synthesized with the understanding of metals that has been gained over the last half century or so. While advanced theory has at times been necessary, is largely presented in an extensive set of Appendixes.

This book deals with three related areas having both fundamental and technological interest. In the first part, the objective is to provide a bird''s­ eye view on structure in polymeric solids. This is then complemented by a chapter, directly technological in its emphasis, dealing with the influence of processing on polymeric materials. In spite of the technological interest, this leads to some of the current fundamental theory. Part II, concerned with liquid crystals, starts with a discussion of the physics of the various types of material, and concludes with a treatment of optical applications. Again, aspects of the theory are stressed though this part is basically phenomenological in character. In Part III, an account is given first of the use of chemical-bonding arguments in understanding the electronic structure of low-dimensional solids, followed by a comprehensive treatment of the influence of dimen­ sionality on phase transitions. A brief summary of dielectric screening in low-dimensional solids follows. Space-charge layers are then treated, including semiconductor inversion layers. Effects of limited dimensionality on superconductivity are also emphasized. Part IV concludes the volume with two specialized topics: electronic structure of biopolymers, and topological defects and disordered systems. The Editors wish to acknowledge that this book had its origins in the material presented at a course organized by the International Centre for Theoretical Physics, Trieste.

There is considerable interest, both fundamental and technological, in the way atoms and molecules interact with solid surfaces. Thus the description of heterogeneous catalysis and other surface reactions requires a detailed understand­ ing of molecule-surface interactions. The primary aim of this volume is to provide fairly broad coverage of atoms and molecules in interaction with a variety of solid surfaces at a level suitable for graduate students and research workers in condensed matter physics, chemical physics, and materials science. The book is intended for experimental workers with interests in basic theory and concepts and had its origins in a Spring College held at the International Centre for Theoretical Physics, Miramare, Trieste. Valuable background reading can be found in the graduate-Ievel introduction to the physics of solid surfaces by ZangwilI(1) and in the earlier works by Garcia­ Moliner and F1ores(2) and Somorjai.(3) For specifically molecule-surface interac­ tions, additional background can be found in Rhodin and Ertl(4) and March.(S) V. Bortolani N. H. March M. P. Tosi References 1. A. Zangwill, Physics at Surfaces, Cambridge University Press, Cambridge (1988). 2. F. Garcia-Moliner and F. Flores, Introduction to the Theory of Solid Surfaces, Cambridge University Press, Cambridge (1979). 3. G. A. Somorjai, Chemistry in Two Dimensions: Surfaces, Cornell University Press, Ithaca, New York (1981). 4. T. N. Rhodin and G. Erd, The Nature of the Surface Chemical Bond, North-Holland, Amsterdam (1979). 5. N. H. March, Chemical Bonds outside Metal Surfaces, Plenum Press, New York (1986).

There is considerable interest, both fundamental and technological, in the way atoms and molecules interact with solid surfaces. Thus the description of heterogeneous catalysis and other surface reactions requires a detailed understand­ ing of molecule-surface interactions. The primary aim of this volume is to provide fairly broad coverage of atoms and molecules in interaction with a variety of solid surfaces at a level suitable for graduate students and research workers in condensed matter physics, chemical physics, and materials science. The book is intended for experimental workers with interests in basic theory and concepts and had its origins in a Spring College held at the International Centre for Theoretical Physics, Miramare, Trieste. Valuable background reading can be found in the graduate-Ievel introduction to the physics of solid surfaces by ZangwilI(1) and in the earlier works by Garcia­ Moliner and F1ores(2) and Somorjai.(3) For specifically molecule-surface interac­ tions, additional background can be found in Rhodin and Ertl(4) and March.(S) V. Bortolani N. H. March M. P. Tosi References 1. A. Zangwill, Physics at Surfaces, Cambridge University Press, Cambridge (1988). 2. F. Garcia-Moliner and F. Flores, Introduction to the Theory of Solid Surfaces, Cambridge University Press, Cambridge (1979). 3. G. A. Somorjai, Chemistry in Two Dimensions: Surfaces, Cornell University Press, Ithaca, New York (1981). 4. T. N. Rhodin and G. Erd, The Nature of the Surface Chemical Bond, North-Holland, Amsterdam (1979). 5. N. H. March, Chemical Bonds outside Metal Surfaces, Plenum Press, New York (1986).

This book has its origins in the 1982 Spring College held at the Interna­ tional Centre for Theoretical Physics, Miramare, Trieste. The primary aim is to give a broad coverage of liquids and amorphous solids, at a level suitable for graduate students and research workers in condensed-matter physics, physical chemistry, and materials science. The book is intended for experimental workers with interests in the basic theory. While the topics covered are many, it was planned to place special emphasis on both static structure and dynamics, including electronic transport. This emphasis is evident from the rather complete coverage of the determination of static structure from both diffraction experiments and, for amorphous solids especially, from model building. The theory of the structure of liquids and liquid mixtures is then dealt with from the standpoint of, first, basic statistical mechanics and, subsequently, pair potentials constructed from the electron theory of simple metals and their alloys. The discussion of static structure is completed in two chapters with rather different emphases on liquid surfaces and interfaces. The first deals with the basic statistical mechanics of neutral and charged interfaces, while the second is concerned with solvation and double-layer effects. Dynamic structure is introduced by a comprehensive discussion of single-particle motion in liquids. This is followed by the structure and dynamics of charged fluids, where again much basic statistical mechanics is developed.

This book has its origins in the 1982 Spring College held at the Interna­ tional Centre for Theoretical Physics, Miramare, Trieste. The primary aim is to give a broad coverage of liquids and amorphous solids, at a level suitable for graduate students and research workers in condensed-matter physics, physical chemistry, and materials science. The book is intended for experimental workers with interests in the basic theory. While the topics covered are many, it was planned to place special emphasis on both static structure and dynamics, including electronic transport. This emphasis is evident from the rather complete coverage of the determination of static structure from both diffraction experiments and, for amorphous solids especially, from model building. The theory of the structure of liquids and liquid mixtures is then dealt with from the standpoint of, first, basic statistical mechanics and, subsequently, pair potentials constructed from the electron theory of simple metals and their alloys. The discussion of static structure is completed in two chapters with rather different emphases on liquid surfaces and interfaces. The first deals with the basic statistical mechanics of neutral and charged interfaces, while the second is concerned with solvation and double-layer effects. Dynamic structure is introduced by a comprehensive discussion of single-particle motion in liquids. This is followed by the structure and dynamics of charged fluids, where again much basic statistical mechanics is developed.

In this introductory chemical physics textbook, the authors discuss the interactions, bonding, electron density, and experimental techniques of free molecules, and apply spectroscopic methods to determine molecular parameters, dynamics, and chemical reactions.

In this introductory chemical physics textbook, the authors discuss the interactions, bonding, electron density, and experimental techniques of free molecules, and apply spectroscopic methods to determine molecular parameters, dynamics, and chemical reactions.

This book is concerned primarily with the fundamental theory underlying the physical and chemical properties of crystalIine semiconductors. After basic introductory material on chemical bonding, electronic band structure, phonons, and electronic transport, some emphasis is placed on surface and interfacial properties, as weil as effects of doping with a variety of impurities. Against this background, the use of such materials in device physics is examined and aspects of materials preparation are discussed briefty. The level of presentation is suitable for postgraduate students and research workers in solid-state physics and chemistry, materials science, and electrical and electronic engineering. Finally, it may be of interest to note that this book originated in a College organized at the International Centre for Theoretical Physics, Trieste, in Spring 1984. P. N. Butcher N. H. March M. P. Tosi vii Contents 1. Bonds and Bands in Semiconductors 1 E. Mooser 1. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 2. The Semiconducting Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 3. Bond Approach Versus Band Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 4. Construction of the Localized X by Linear Combination of n Atomic Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1. 5. The General Octet Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1. 6. The Aufbau-Principle of the Crystal Structure of Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1. 7. A Building Principle for Polyanionic Structures . . . . . . . . . . . . . . . . . . . . . . 29 I. H. Structural Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1. 9. Chemical Bonds and Semiconductivity in Transition-Element Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1. 10. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2. Electronic Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 G. Grosso 2. 1. Two Different Strategies for Band-Structure Calculations . . . . . . . 55 2. 2. The Tight-Binding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This book is concerned primarily with the fundamental theory underlying the physical and chemical properties of crystalIine semiconductors. After basic introductory material on chemical bonding, electronic band structure, phonons, and electronic transport, some emphasis is placed on surface and interfacial properties, as weil as effects of doping with a variety of impurities. Against this background, the use of such materials in device physics is examined and aspects of materials preparation are discussed briefty. The level of presentation is suitable for postgraduate students and research workers in solid-state physics and chemistry, materials science, and electrical and electronic engineering. Finally, it may be of interest to note that this book originated in a College organized at the International Centre for Theoretical Physics, Trieste, in Spring 1984. P. N. Butcher N. H. March M. P. Tosi vii Contents 1. Bonds and Bands in Semiconductors 1 E. Mooser 1. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 2. The Semiconducting Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 3. Bond Approach Versus Band Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 4. Construction of the Localized X by Linear Combination of n Atomic Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1. 5. The General Octet Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1. 6. The Aufbau-Principle of the Crystal Structure of Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1. 7. A Building Principle for Polyanionic Structures . . . . . . . . . . . . . . . . . . . . . . 29 I. H. Structural Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1. 9. Chemical Bonds and Semiconductivity in Transition-Element Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1. 10. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2. Electronic Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 G. Grosso 2. 1. Two Different Strategies for Band-Structure Calculations . . . . . . . 55 2. 2. The Tight-Binding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The theory of the inhomogeneous electron gas had its origin in the Thomas­ Fermi statistical theory, which is discussed in the first chapter of this book. This already leads to significant physical results for the binding energies of atomic ions, though because it leaves out shell structure the results of such a theory cannot reflect the richness of the Periodic Table. Therefore, for a long time, the earlier method proposed by Hartree, in which each electron is assigned its own personal wave function and energy, dominated atomic theory. The extension of the Hartree theory by Fock, to include exchange, had its parallel in the density description when Dirac showed how to incorporate exchange in the Thomas-Fermi theory. Considerably later, in 1951, Slater, in an important paper, showed how a result similar to but not identical with that of Dirac followed as a simplification of the Hartree-Fock method. It was Gombas and other workers who recognized that one could also incorporate electron correlation consistently into the Thomas-Fermi-Dirac theory by using uniform electron gas relations locally, and progress had been made along all these avenues by the 1950s.

The theory of the inhomogeneous electron gas had its origin in the Thomas­ Fermi statistical theory, which is discussed in the first chapter of this book. This already leads to significant physical results for the binding energies of atomic ions, though because it leaves out shell structure the results of such a theory cannot reflect the richness of the Periodic Table. Therefore, for a long time, the earlier method proposed by Hartree, in which each electron is assigned its own personal wave function and energy, dominated atomic theory. The extension of the Hartree theory by Fock, to include exchange, had its parallel in the density description when Dirac showed how to incorporate exchange in the Thomas-Fermi theory. Considerably later, in 1951, Slater, in an important paper, showed how a result similar to but not identical with that of Dirac followed as a simplification of the Hartree-Fock method. It was Gombas and other workers who recognized that one could also incorporate electron correlation consistently into the Thomas-Fermi-Dirac theory by using uniform electron gas relations locally, and progress had been made along all these avenues by the 1950s.

This book had its origins in lectures presented at EPFL, Lausanne, during two separate visits (the most recent being to IRRMA). The author is most grateful to Professors A. Baldereschi, R. Car, and A. Quattropani for making these visits possible, and for the splendidly stimulating environment provided. Professors S. Baroni and R. Resta also influenced considerably the presentation of material by constructive help and comments. Most importantly, Chapters 4 and 5 were originally prepared for a review article by Professor G. Senatore, then at Pavia and now in Trieste, and myself for Reviews of Modem Physics (1994). In the ''course of this collaboration, he has taught me a great deal, especially about quantum Monte Carlo procedures, and Chapter 5 is based directly on this review article. Also in Chapter 4, my original draft on Gutzwiller''s method has been transformed by his deeper understanding; again this is reflected directly in Chapter 4; especially in the earlier sections. In addition to the above background, it is relevant here to point out that, as a backcloth for the present, largely "state of the art," account, there are two highly relevant earlier books: The Many-body Problem in Quantum Mechanics with W.

This book had its origins in lectures presented at EPFL, Lausanne, during two separate visits (the most recent being to IRRMA). The author is most grateful to Professors A. Baldereschi, R. Car, and A. Quattropani for making these visits possible, and for the splendidly stimulating environment provided. Professors S. Baroni and R. Resta also influenced considerably the presentation of material by constructive help and comments. Most importantly, Chapters 4 and 5 were originally prepared for a review article by Professor G. Senatore, then at Pavia and now in Trieste, and myself for Reviews of Modem Physics (1994). In the 'course of this collaboration, he has taught me a great deal, especially about quantum Monte Carlo procedures, and Chapter 5 is based directly on this review article. Also in Chapter 4, my original draft on Gutzwiller's method has been transformed by his deeper understanding; again this is reflected directly in Chapter 4; especially in the earlier sections. In addition to the above background, it is relevant here to point out that, as a backcloth for the present, largely "state of the art," account, there are two highly relevant earlier books: The Many-body Problem in Quantum Mechanics with W.

This volume is concerned with the theoretical description of patterns and instabilities and their relevance to physics, chemistry, and biology. More specifically, the theme of the work is the theory of nonlinear physical systems with emphasis on the mechanisms leading to the appearance of regular patterns of ordered behavior and chaotic patterns of stochastic behavior. The aim is to present basic concepts and current problems from a variety of points of view. In spite of the emphasis on concepts, some effort has been made to bring together experimental observations and theoretical mechanisms to provide a basic understanding of the aspects of the behavior of nonlinear systems which have a measure of generality. Chaos theory has become a real challenge to physicists with very different interests and also in many other disciplines, of which astronomy, chemistry, medicine, meteorology, economics, and social theory are already embraced at the time of writing. The study of chaos-related phenomena has a truly interdisciplinary charac­ ter and makes use of important concepts and methods from other disciplines. As one important example, for the description of chaotic structures the branch of mathematics called fractal geometry (associated particularly with the name of Mandelbrot) has proved invaluable. For the discussion of the richness of ordered structures which appear, one relies on the theory of pattern recognition. It is relevant to mention that, to date, computer studies have greatly aided the analysis of theoretical models describing chaos.

This volume is concerned with the theoretical description of patterns and instabilities and their relevance to physics, chemistry, and biology. More specifically, the theme of the work is the theory of nonlinear physical systems with emphasis on the mechanisms leading to the appearance of regular patterns of ordered behavior and chaotic patterns of stochastic behavior. The aim is to present basic concepts and current problems from a variety of points of view. In spite of the emphasis on concepts, some effort has been made to bring together experimental observations and theoretical mechanisms to provide a basic understanding of the aspects of the behavior of nonlinear systems which have a measure of generality. Chaos theory has become a real challenge to physicists with very different interests and also in many other disciplines, of which astronomy, chemistry, medicine, meteorology, economics, and social theory are already embraced at the time of writing. The study of chaos-related phenomena has a truly interdisciplinary charac­ ter and makes use of important concepts and methods from other disciplines. As one important example, for the description of chaotic structures the branch of mathematics called fractal geometry (associated particularly with the name of Mandelbrot) has proved invaluable. For the discussion of the richness of ordered structures which appear, one relies on the theory of pattern recognition. It is relevant to mention that, to date, computer studies have greatly aided the analysis of theoretical models describing chaos.

Presenting the latest advances in artificial structures, this volume discusses in-depth the structure and electron transport mechanisms of quantum wells, superlattices, quantum wires, and quantum dots. It will serve as an invaluable reference and review for researchers and graduate students in solid-state physics, materials science, and electrical and electronic engineering.

Presenting the latest advances in artificial structures, this volume discusses in-depth the structure and electron transport mechanisms of quantum wells, superlattices, quantum wires, and quantum dots. It will serve as an invaluable reference and review for researchers and graduate students in solid-state physics, materials science, and electrical and electronic engineering.