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Author: Viraht Sahni
Publisher: Springer Nature
ISBN: 303097409X
Category : Science
Languages : en
Pages : 415
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Book Description
This book presents a complementary perspective to Schrödinger theory of electrons in an electromagnetic field, one that does not appear in any text on quantum mechanics. The perspective, derived from Schrödinger theory, is that of the individual electron in the sea of electrons via its temporal and stationary-state equations of motion – the ‘Quantal Newtonian’ Second and First Laws. The Laws are in terms of ‘classical’ fields experienced by each electron, the sources of the fields being quantum-mechanical expectation values of Hermitian operators taken with respect to the wave function. Each electron experiences the external field, and internal fields representative of properties of the system, and a field descriptive of its response. The energies are obtained in terms of the fields. The ‘Quantal Newtonian’ Laws lead to physical insights, and new properties of the electronic system are revealed. New mathematical understandings of Schrödinger theory emerge which show the equation to be intrinsically self-consistent. Another complimentary perspective to Schrödinger theory is its manifestation as a local effective potential theory described via Quantal Density Functional theory. This description too is in terms of ‘classical’ fields and quantal sources. The theory provides a rigorous physical explanation of the mapping from the interacting system to the local potential theory equivalent. The complementary perspective to stationary ground state Schrödinger theory founded in the theorems of Hohenberg and Kohn, their extension to the presence of a magnetic field and to the temporal domain – Modern Density Functional Theory -- is also described. The new perspectives are elucidated by application to analytically solvable interacting systems. These solutions and other relevant wave function properties are derived.
Author: Viraht Sahni
Publisher: Springer Nature
ISBN: 303097409X
Category : Science
Languages : en
Pages : 415
Get Book Here
Book Description
This book presents a complementary perspective to Schrödinger theory of electrons in an electromagnetic field, one that does not appear in any text on quantum mechanics. The perspective, derived from Schrödinger theory, is that of the individual electron in the sea of electrons via its temporal and stationary-state equations of motion – the ‘Quantal Newtonian’ Second and First Laws. The Laws are in terms of ‘classical’ fields experienced by each electron, the sources of the fields being quantum-mechanical expectation values of Hermitian operators taken with respect to the wave function. Each electron experiences the external field, and internal fields representative of properties of the system, and a field descriptive of its response. The energies are obtained in terms of the fields. The ‘Quantal Newtonian’ Laws lead to physical insights, and new properties of the electronic system are revealed. New mathematical understandings of Schrödinger theory emerge which show the equation to be intrinsically self-consistent. Another complimentary perspective to Schrödinger theory is its manifestation as a local effective potential theory described via Quantal Density Functional theory. This description too is in terms of ‘classical’ fields and quantal sources. The theory provides a rigorous physical explanation of the mapping from the interacting system to the local potential theory equivalent. The complementary perspective to stationary ground state Schrödinger theory founded in the theorems of Hohenberg and Kohn, their extension to the presence of a magnetic field and to the temporal domain – Modern Density Functional Theory -- is also described. The new perspectives are elucidated by application to analytically solvable interacting systems. These solutions and other relevant wave function properties are derived.
Author: Roman F. Nalewajski
Publisher: Springer Science & Business Media
ISBN: 3642201806
Category : Science
Languages : en
Pages : 727
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Book Description
The understanding in science implies insights from several different points of view. Alternative modern outlooks on electronic structure of atoms and molecules, all rooted in quantum mechanics, are presented in a single text. Together these complementary perspectives provide a deeper understanding of the localization of electrons and bonds, the origins of chemical interaction and reactivity behavior, the interaction between the geometric and electronic structure of molecules, etc. In the opening two parts the basic principles and techniques of the contemporary computational and conceptual quantum chemistry are presented, within both the wave-function and electron-density theories. This background material is followed by a discussion of chemical concepts, including stages of the bond-formation processes, chemical valence and bond-multiplicity indices, the hardness/softness descriptors of molecules and reactants, and general chemical reactivity/stability principles. The insights from Information Theory, the basic elements of which are briefly introduced, including the entropic origins and Orbital Communication Theory of the chemical bond, are the subject of Part IV. The importance of the non-additive (interference) information tools in exploring patterns of chemical bonds and their covalent and ionic components will be emphasized.
Author: Andrii Iurov
Publisher: Springer Nature
ISBN: 3031600657
Category :
Languages : en
Pages : 389
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Book Description
Author: Stanley Raimes
Publisher: North-Holland
ISBN:
Category : Science
Languages : en
Pages : 292
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Book Description
Author: Henry A. Bent
Publisher: Trafford Publishing
ISBN: 1490714073
Category : Juvenile Nonfiction
Languages : en
Pages : 303
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Book Description
MOLECULES and the Chemical Bond is about understanding Schrdingers equation, for chemical systems. In his famous Lectures on Physics, Richard Feynman quotes Paul Dirac on what it means to understand an equation. I understand what an equation means, said Dirac, if I have a way of figuring out the characteristics of its solutions without actually solving it. That hits the nail on the head! Its precisely what Conceptual Valence Bond Theory does for Schrdingers equation. A physical understanding of an equation, adds Feynman, is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist. It unfolds in MCB in two stages, described by Newton as a stage of Analysis (a union of observations and inductions) and a stage of Synthesis (use of inductions, accepted as first principles, to explain observations). The books chief vehicle for creating an intuitive understanding of solutions of Schrdingers equation is the worlds largest and to the authors knowledge, virtually only library of line drawings of exclusive orbital models of chemical species electron density profiles. By focussing attention on fundamental physical principles and by avoiding use of atomic orbitals and, thereby, mathematical complexities associated with Schrdingers equation (the only source of atomic orbitals), the books essays provide a scientifically sound, student-friendly introduction to modern valence theory. Repetition of fundamental ideas, here and there, is intended to make individual essays understandable and interesting, each by itself, so that readers may examine them in any order, in leisurely walks, so to speak, in the big garden that is valence theory, picking bouquets to their liking.
Author: Erwin Schrödinger
Publisher: American Mathematical Soc.
ISBN: 0821835246
Category : Mathematics
Languages : en
Pages : 226
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Book Description
The famous equation that bears Erwin Schrödinger's name encapsulates his profound contributions to quantum mechanics using wave mechanics. This third, augmented edition of his papers on the topic contains the six original, famous papers in which Schrödinger created and developed the subject of wave mechanics as published in the original edition. As the author points out, at the time each paper was written the results of the later papers were largely unknown to him. This edition also contains three papers that were written shortly after the original edition was published and four lectures delivered by Schrödinger at the Royal Institution in London in 1928. The papers and lectures in this volume were revised by the author and translated into English, and afford the reader a striking and valuable insight into how wave mechanics developed.
Author: D. Hestenes
Publisher: Springer Science & Business Media
ISBN: 9401135703
Category : Science
Languages : en
Pages : 405
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Book Description
techniques, and raises new issues of physical interpretation as well as possibilities for deepening the theory. (3) Barut contributes a comprehensive review of his own ambitious program in electron theory and quantum electrodynamics. Barut's work is rich with ingenious ideas, and the interest it provokes among other theorists can be seen in the cri tique by Grandy. Cooperstock takes a much different approach to nonlinear field-electron coupling which leads him to conclusions about the size of the electron. (4) Capri and Bandrauk work within the standard framework of quantum electrodynamics. Bandrauk presents a valuable review of his theoretical approach to the striking new photoelectric phenomena in high intensity laser experiments. (5) Jung proposes a theory to merge the ideas of free-free transitions and of scattering chaos, which is becoming increasingly important in the theoretical analysis of nonlinear optical phenomena. For the last half century the properties of electrons have been probed primarily by scattering experiments at ever higher energies. Recently, however, two powerful new experimental techniques have emerged capable of giving alternative experimental views of the electron. We refer to (1) the confinement of single electrons for long term study, and (2) the interaction of electrons with high intensity laser fields. Articles by outstanding practitioners of both techniques are included in Part II of these Proceedings. The precision experiments on trapped electrons by the Washington group quoted above have already led to a Nobel prize for the most accurate measurements of the electron magnetic moment.
Author: John Stringer
Publisher: Franklin Book Company
ISBN:
Category : Science
Languages : en
Pages : 260
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Book Description
The breakdown of classical theory -- Atomic spectra and the old quantum theory -- The uncertainty principle of Heisenberg -- The foundations of quantum mechanics -- Some problems in wave mechanics -- A wave-mechanical treatment of the simple harmonic oscillator and the hydrogen atom -- Assemblies of atoms -- Atoms in motion -- Statistical mechanics -- Simple models of metals -- The band theory of solids -- Some results of band theory.
Author: Olimpia Lombardi
Publisher: Springer Nature
ISBN: 3030983730
Category : Science
Languages : en
Pages : 256
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Book Description
This book explores the philosophy and the foundations of quantum chemistry. It features chapters written by experts in the field. The contributions analyze quantum chemistry as a discipline, in particular, its relation with both chemistry and physics from the viewpoint of realism and reduction. Coverage includes such topics as quantum chemistry as an “in-between” discipline, molecular structure and quantum mechanics, quantum chemical models, and atoms and molecules in quantum chemistry. The interest of this book is twofold. First, the contributions aim to update and refresh the discussions regarding the foundations of quantum chemistry. Second, they seek to develop new philosophical perspectives that this discipline can suggest to philosophers of science. From its origins, quantum chemistry filled a problematic position in the disciplinary space. On the one hand, it is a branch of theoretical chemistry. On the other hand, it appeals essentially to theoretical tools coming from physics. This peculiar position triggered conceptual questions about its own identity. Inside this book, readers will find updated discussions on the foundations and the philosophy of this complex discipline.
Author: Simon Grabowsky
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311066027X
Category : Science
Languages : en
Pages : 412
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Book Description
As chemical bonds are not observable, there are various theories and models for their description. This book presents a selection of conceptually very different and historically competing views on chemical bonding analysis from quantum chemistry and quantum crystallography. It not only explains the principles and theories behind the methods, but also provides practical examples of how to derive bonding descriptors with modern software and of how to interpret them.
