Principles of Quantum Scattering Theory  book cover
1st Edition

Principles of Quantum Scattering Theory

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ISBN 9780750304962
Published December 1, 2003 by CRC Press
392 Pages

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Book Description

Scattering is one of the most powerful methods used to study the structure of matter, and many of the most important breakthroughs in physics have been made by means of scattering. Nearly a century has passed since the first investigations in this field, and the work undertaken since then has resulted in a rich literature encompassing both experimental and theoretical results.

In scattering, one customarily studies collisions among nuclear, sub-nuclear, atomic or molecular particles, and as these are intrinsically quantum systems, it is logical that quantum mechanics is used as the basis for modern scattering theory. In Principles of Quantum Scattering Theory, the author judiciously combines physical intuition and mathematical rigour to present various selected principles of quantum scattering theory. As always in physics, experiment should be used to ultimately validate physical and mathematical modelling, and the author presents a number of exemplary illustrations, comparing theoretical and experimental cross sections in a selection of major inelastic ion-atom collisions at high non-relativistic energies.

Quantum scattering theory, one of the most beautiful theories in physics, is also very rich in mathematics. Principles of Quantum Scattering Theory is intended primarily for graduate physics students, but also for non-specialist physicists for whom the clarity of exposition should aid comprehension of these mathematical complexities.

Table of Contents

PART I; The main principles and the basic theoretical frameworks for a nonrelativistic quantum-mechanical theory of scattering; A Introduction; B The main physical features of collision problems; B.1 Recognizable reference points of scattering theory; C Universality of the scattering problem; C.1 Fundamental aspects of collision theory; C.2 Collisions in various branches of physics; C.3 Importance of collisions in atomic and molecular physics; C.4 Collisions and new sources of energy; C.5 Application of collisional phenomena in other sciences; C.6 Application of collision phenomena in technology; 1 The key features of quantum systems and the Kato conditions; 2 Time evolution of quantum systems; 3 The Schrodinger picture; 4 The Heisenberg picture; 5 The Dirac picture; 6 The Dyson perturbation expansion of the evolution operator; 7 Time-dependent scattering theory; 8 Time-independent scattering theory; 9 The problem of asymptotic convergence of scattering states; 10 The principle of detailed balance; 11 Convergence of series of operators, state vectors and matrix elements; 12 Recapitulation of the principles of quantum scattering theory; 13 Summary to part I; PART II Selected applications of non-relativistic quantum scattering theory to energetic inelastic collisions of ions with atoms; 14 The physics of double scatterings; 15 The leading experimental methods for double scatterings; 16 The two main theoretical frameworks for ion-atom collisions from low to high energies; 17 Basic mechanisms behind elementary atomic processes; 18 Direct momentum matching; 19 Indirect momentum matching; 20 Dynamic electron correlations; 21 Thomas double scatterings of the active electron with two atomic nuclei; 22 The impulse hypothesis; 23 Drawbacks of the continuum distorted wave method and its; 'derivatives'; 24 Coulomb-Born-type methods for electron detachment; 25 A variational unification of low- and high-energy methods; 26 Thomas-like dielectronic scatterings in transfer ionization; 27 Projectile and target merged cold beams for highly correlated events; 28 Thomas double scatterings of atoms in ion-molecule collisions; 29 Collisions of cold ions and Bose-Einstein condensates; 30 Fundamental reasons for the equivalence between the classical Thomas successive binary collisions and quantal double scatterings; 31 Multiple ionization in fast ion-atom and ion-molecule collisions; 32 Recapitulation on double-scattering mechanisms; 33 The reasons for the inadequacy of the standard impulse approximation; 34 The reformulated impulse approximation (RIA); 35 An analytical calculation of the main scattering integral; 36 Correlated electronic dynamics at all energies; 37 Correct links between scattered waves and transition operator potentials; 38 Illustrations; 38.1 Computational methods; 38.1.1 Deterministic methods; 38.1.2 Stochastic methods; 38.2 Atomic collision problems; 39 Summary to part II; 40 Outlook; References; Index

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"…presents a thorough overview of the main aspects of the subject…highly recommended…important acquisition for defense libraries and other science and technology libraries…"
E-Streams, Volume 8, no. 8, 2005
"Never have the principles of scattering theory been formulated and applied to such a breadth of problems from basic physics to condenced matter, bio, chemical and medical physics. Computational strategies emphasize both deterministic stochastic methods adding to the value of the book".

-- Erkki Brandas

"This is an excellent book."

-- Professor Ivan Mancev