The Quantum Theory of Scattering

M. F. Werby

The scattering of waves in classical physics and quantum scattering theory have many dissimilarities, but also many things in common. Many of the modern developments in classical wave theory have their origin in quantum scattering despite the later development of quantum physics. Although each field has diverged from the other over time, there are many analogies between the two disciplines and much in one area may enhance the other. In this work an outline is given of some aspects of the classical scattering theory of waves which have some relation with quantum theory. In addition, some numerical techniques are presented that may be of use in both areas.

A.S. Davydov

V. K. Ignatovich

The standard scattering theory (SST) in non relativistic quantum mechanics (QM) is analyzed. Self-contradictions of SST are deconstructed. A direct way to calculate scattering probability without introduction of a finite volume is discussed. Substantiation of SST in textbooks with the help of wave packets is shown to be incomplete. A complete theory of wave packets scattering on a fixed center is presented, and its similarity to the plane wave scattering is demonstrated. The neutron scattering on a monatomic gas is investigated, and several problems are pointed out. A catastrophic ambiguity of the cross section is revealed, and a way to resolve this ambiguity is discussed.

S. Zienau

Dževad Belkić

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.

Leonard S. Rodberg, Roy M. Thaler, William J. Camp