Approximate Potential Calculations in Molecular Scattering Theory
Author : Timothy Glen Mattson
Publisher :
Page : 400 pages
File Size : 28,18 MB
Release : 1985
Category : Quantum chemistry
ISBN :
Scattering Theory of Molecules, Atoms, and Nuclei
Author : Luiz Felipe Canto
Publisher : World Scientific
Page : 646 pages
File Size : 40,57 MB
Release : 2013
Category : Science
ISBN : 9814329835
Book Description
The aim of the book is to give a coherent and comprehensive account of quantum scattering theory with applications to atomic, molecular and nuclear systems. The motivation for this is to supply the necessary theoretical tools to calculate scattering observables of these many-body systems. Concepts, which are seemingly different for the atomic/molecular scattering from those for nuclear systems, are shown to be the same once the physical units such as energy, length are diligently clarified. Many-body resonances excited in nuclear systems are the same as those in atomic systems and come under the name of Feshbach resonances. We clarify this. We also lean heavily on semi-classical methods to explain the physics of quantum scattering and especially the interference seen in the angle dependence of the cross section. Having in mind a wider readership, the book includes sections on scattering in two dimensions, which is of use in surface physics. Several problems are also included at the end of each of the chapters.
Potential Scattering in Atomic Physics
Author : P. G. Burke
Publisher : Springer Science & Business Media
Page : 137 pages
File Size : 50,19 MB
Release : 2012-12-06
Category : Science
ISBN : 1461341124
Book Description
This monograph was written while the author was a visitor at the Center for Theoretical Studies at the University of Miami, Coral Gables, Florida. The author wishes to thank Professor Behram Kursunoglu for the warm hospitality extended to him at the Center and to acknowledge the many interesting and fruitful discussions which he had with other visitors and with members of staff at the Center. Philip G. Burke v Contents 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Scattering by a Short-Range Potential. . . . . . . . . . . . . . . 5 3. Scattering by a Coulomb Potential. . . . . . . . . . . . . . . . . . 11 4. Scattering by a Spin-Orbit Potential . . . . . . . . . . . . . . " 17 5. Scattering by One-Electron Atoms. . . . . . . . . . . . . . . . . . 23 6. Low-Energy Effective-Range Theory. . . . . . . . . . . . . . . . 39 7. Bound States and Resonances. . . . . . . . . . . . . . . . . . . . . . 55 8. Variational Methods and Bound Principles. . . . . . . . . . 75 9. Integral Equation Methods and the Born Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 10. Semiclassical and Eikonal Methods . . . . . . . . . . . . . . . . . 117 Appendix. The Coupling of Angular Momenta . . . . . . . . . . . 127 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 vii 1 Introduction In this monograph we study the scattering of a particle by a potential field with particular reference to elastic electron scat tering by a neutral atom or by an ion. This subject is clearly of interest in its own right as a branch of quantum mechanical scattering theory. However, it also serves as an introduction to many of the basic theoretical concepts which are used in inelastic electron scattering and ionization. Consequently this mono graph can be viewed as an introduction to texts where these subjects are treated.
Algorithms and Computer Codes for Atomic and Molecular Quantum Scattering Theory
Author :
Publisher :
Page : 434 pages
File Size : 36,93 MB
Release : 1979
Category : Algorithms
ISBN :
Book Description
Semiclassical Theories of Molecular Scattering
Author : B. C. Eu
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 11,94 MB
Release : 2012-12-06
Category : Science
ISBN : 3642881653
Book Description
The study of molecular collisions at energies from less than about 100 eV 3 down to a few 10- eV, which is roughly the range of chemical interest, has greatly expanded in the last 10 to 20 years. As in many fields, this activity has been stimulated by parallel advances in theory which have triggered the autocatalytic positive feedback system of experiment challenging theory and vice versa. Possibly the biggest driving force, however, has been the growing awareness that molecular collisions are important in our understanding of na tural and man-made environments. Molecular collision dynamics is now studied in connection with molecular formation in interplanetary space, upper atmo sphere chemistry, plasmas, lasers and fusion reactors, and is crucial for understanding gas-dynamic flow processes, gas-phase chemical reactions and catalysis. Despite the great strides made in studying elementary collisions in laboratory scattering experiments, many of the processes in these areas are too complicated for us to hope ever to study them in detail in the labo ratory. Thus in the long run we shall have to rely on theory. Initially, I think many of us, like myself, had hoped that the development of fast compu ters would outpace the demands on computing time so that "brute force" quan tum-mechanical exact calculations would provide all the answers. Unfortunate ly this has not been the case and efficient approximations are needed. They can be broadly classified as classical, semiclassical or semiquantal.
The Transfer of Molecular Energies by Collision: Recent Quantum Treatments
Author : F. A. Gianturco
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 36,42 MB
Release : 2012-12-06
Category : Science
ISBN : 3642931227
Book Description
I I These Lecture Notes are intended as an introduction to the theoretical formulation and computational aspects of the molecular energy transfer processes which take place in an increasingly sophisticated range of molecular scattering experiments. They are directed to chemistry graduate students and emphasize the quantum mechanical approach, with little or no attention to classical and semi classical treatments or to formal presentations. Several Sections of the first Chapters are based on lectures given at the Graduate School of Physics of the University of Genoa a few years ago and I thank the students for their sense of duty in following to the end all those no tation-filled blackboards and transparencies. The kind patience of my wife Carolyn in reading the whole manuscript and improving its form is gratefully acknowledged. Franco A. Gianturco Bari, September 1978 CON TEN T S FOREWORD I NTRODUCTI ON Page 1. A RESUME OF QUANTUM MECHANICAL POTENTIAL SCATTERING 1. 1. General formulation of the problem Page 5 1. 2. Solutions of the radial equation 10 " 1. 3. The method of partial waves 13 1. 4. Some properties of 61. The Born appro~imation 18 1. 5. Properties of the S-matrix: bound states and resonances 23 1. 6. Classical and semiclassical scattering,a set of defi- tions 34 References 44 2. POTENTIAL ENERGY HYPERSURFACE CALCULATIONS FOR SIMPLE SYSTEMS 2. 1. Kinematic considerations 45 2. 2. General development of a priori method 52 2. 3. Some approximate treatments 68 2. 4.
Quantum Theory Of Tunneling
Author : Mohsen Razavy
Publisher : World Scientific
Page : 574 pages
File Size : 43,34 MB
Release : 2003-01-29
Category : Science
ISBN : 9814488445
Book Description
This book provides a comprehensive introduction to the theoretical foundations of quantum tunneling, stressing the basic physics underlying the applications. The topics addressed include exponential and nonexponential decay processes and the application of scattering theory to tunneling problems. In addition to the Schrödinger equation approach, the path integral, Heisenberg's equations and the phase space method are all used to study the motion of a particle under the barrier. Extensions to the multidimensional cases and tunneling of particles with internal degrees of freedom are also considered. Furthermore, recent advances concerning time delay and tunneling times and some of the problems associated with their measurement are also discussed. Finally, some examples of tunneling in atomic, molecular, nuclear and condensed matter physics are presented.
Theory of Electron—Atom Collisions
Author : Philip G. Burke
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 49,39 MB
Release : 2013-06-29
Category : Science
ISBN : 1489915672
Book Description
The authors aim to hone the theory of electron-atom and electron-ion collisions by developing mathematical equations and comparing their results to the wealth of recent experimental data. This first of three parts focuses on potential scattering, and will serve as an introduction to many of the concepts covered in Parts II and III. As these processes occur in so many of the physical sciences, researchers in astrophysics, atmospheric physics, plasma physics, and laser physics will all benefit from the monograph.
Scattering Theory
Author : Harald Friedrich
Publisher : Springer
Page : 293 pages
File Size : 18,4 MB
Release : 2015-11-20
Category : Science
ISBN : 3662485265
Book Description
This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is kept as low as at all possible and deeper questions related to the mathematical foundations of scattering theory are passed by. It should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. The book is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
Theory and Application of Quantum Molecular Dynamics
Author : John Z. H. Zhang
Publisher : World Scientific
Page : 390 pages
File Size : 16,82 MB
Release : 1999
Category : Science
ISBN : 9789810233884
Book Description
This book gives an updated and detailed presentation of modern quantum-mechanical treatments and practical computational methods for dynamical processes of small molecular systems. The main emphasis is on the recent development of successful theories and computational methods for the reactive scattering process. Specific applications are given in detail for a number of benchmark chemical reaction systems in the gas phase and gas surface. Differing from traditional physics books focusing on abstract collision theory for elastic collisions, the book has been written in a fashion in which the development of general reactive or rearrangement scattering theory is accompanied by practical applications for realistic reaction systems.
