Direct and Inverse Problems: Potentials in Quantum Scattering - Softcover

Zakhariev, Boris N.; Suzko, Allina A.

Softcover

ISBN 10: 3540524843 ISBN 13: 9783540524847

Publisher: Springer, 1990

Synopsis

Rapid progress in quantum theory brings us new important results which are often not immediately clear to all who need them. But fortunately, this is also followed by simplifications and unifications of our previous concepts. The inverse problem method ("The most beautiful idea of the XX-th century" - Zakharov et aI., 1980) has just both these aspects. It is rather astonishing that it took 50 years after the foundation of quantum mechanics for the creation of the "pictures" showing the direct connection of obser­ vables with interactions. Recently, illustrations of this type began to appear in the literature (e. g., how potentials are deformed with thc shift of one energy level or change of some resonance reduced width). Although they are transparent to those studying the quantum world and can be included within the necessary elements of quantum literacy, they are still largely unknown even to many specialists. For the first time, the most interesting of these pictures enriching our quantum intuition are col­ lected here and placed at your disposal. The readers of this monograph have the advantage of getting the latest information which became available after the publication of the Russian edition. It has been incor­ porated here in the simplest presentation possible. For example, new sections con­ cerning exactly solvable models, including the multi-channel, multi-dimensional ones and with time dependent potentials have been added. The first attempts in solving the three-body inverse problem are also mentioned.

About this title

Product Description

Direct and Inverse Problems This textbook can be viewed as a "how-to" manual for solving quantum inverse problems, for deriving the potential from spectra or scattering data, and as a quantum "picture book" which aims to enhance the reader's quantum intuition.

Synopsis

This textbook can be viewed as a "how-to" manual for solving quantum inverse problems, for deriving the potential from spectra or scattering data, and as a quantum "picture book" which aims to enhance the reader's quantum intuition. The formal exposition of inverse methods is paralleled by a discussion of the direct problem. Differential and finite-difference equations are presented side by side. The common features and advantages of a variety of solution methods are analyzed. To foster a better understanding, the physical meaning of the mathematical quantities are discussed. Wave confinement in continuum bound states, resonance and collective tunnelling, energy shifts and the spectral and phase equivalence of various interactions are some of the physical problems covered.

Edition details

• Publisher: Springer
• Publication date: 1990
• ISBN 10: 3540524843
• ISBN 13: 9783540524847
• Binding: Paperback
• Language: English
• Number of pages: 236