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Series in atomic and molecular physics/Series in atomic molecular physics

Recapitulation of the selected main principles of quantum scattering theory

Published Dec 1, 2003• 0 citations
Publisher
DOI
10.1201/9781420033649.ch12

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Recapitulation of the selected main principles of quantum scattering theory

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This chapter examines the most critical properties, which make the collision phenomenon substantially different from the corresponding problem of bound states in quantum mechanics. In order to elaborate the treatments further in the course of the presented analysis, it was necessary to employ the quantum-mechanical entities, such as the equations of time evolution, as well as the state vectors and the Hilbert space of eigenstates. A given picture of quantum mechanics can be more practical than formalism for the examined physical phenomenon. Hence, the choice of the optimal picture of quantum mechanics becomes a matter of considerable practical importance. The initial state Ψ0i is experimentally prepared, i.e. characterized by means of the impulse, polarization, spin, isospin and other internal quantum numbers of the constituent parts of the scattering system.

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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.

Series in atomic and molecular physics/Series in atomic molecular physics•Dec 1, 2003•58 citations
This chapter examines the most critical properties, which make the collision phenomenon substantially different from the corresponding problem of bound states in quantum mechanics. In order to elaborate the treatments further in the course of the presented analysis, it was necessary to employ the quantum-mechanical entities, such as the equations of time evolution, as well as the state vectors and the Hilbert space of eigenstates. A given picture of quantum mechanics can be more practical than formalism for the examined physical phenomenon. Hence, the choice of the optimal picture of quantum mechanics becomes a matter of considerable practical importance. The initial state Ψ0i is experimentally prepared, i.e. characterized by means of the impulse, polarization, spin, isospin and other internal quantum numbers of the constituent parts of the scattering system.
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.