Jost Functions in Quantum Mechanics (eBook)

Based on Jost function theory this book presents an approach useful for different types of quantum mechanical problems. These include the description of scattering, bound, and resonant states, in a unified way. The reader finds here all that is known about Jost functions as well as what is needed to fill the gap between the pure mathematical theory and numerical calculations. Some of the topics covered are: quantum resonances, Regge poles, multichannel scattering, Coulomb interaction, Riemann surfaces, multichannel analog of the effective range theory, one- and two-dimensional problems, many-body problems within the hyperspherical approach, just to mention few of them. These topics are relevant in the fields of quantum few-body theory, nuclear reactions, atomic collisions, and low-dimensional semiconductor nanostructures. In light of this, the book is meant for students, who study quantum mechanics, scattering theory, or nuclear reactions at the advanced level as well as for post-graduate students and researchers in the fields of nuclear and atomic physics. Many of the arguments that are traditional for textbooks on quantum mechanics and scattering theory, are covered here in a different way, using the Jost functions. This gives the reader a new insight into the subject, revealing new features of various mathematical objects and quantum phenomena.

Sergei Anatoljevich Rakityansky was born in Omsk in 1956. From 1973 to 1978, he studied physics in Tashkent University (USSR). After that, during 19 years (1978 -1997), he worked at the Joint Institute for Nuclear Research (Dubna, Russia). In 1997 he emigrated to South Africa where worked at the University of South Africa (UNISA, Pretoria). Since 2009, he is Professor of Physics at the University of Pretoria. His research focusses on scattering theory, theory of quantum resonances, and on nuclear reactions. On such topics he authored more than 60 scientific papers in peer-reviewed journals.