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Jost functions in quantum mechanics : a unified approach to scattering, bound, and resonant state problems / Sergei A. Rakityansky.

Rakityansky, Sergei A., author.
2022
QC174.17.M35
Available Online
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Title
Jost functions in quantum mechanics : a unified approach to scattering, bound, and resonant state problems / Sergei A. Rakityansky.
Author
Rakityansky, Sergei A., author.
ISBN
9783031077616 (electronic bk.)
303107761X (electronic bk.)
9783031077609
3031077601
DOI
https://doi.org/10.1007/978-3-031-07761-6
Published
Cham : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource (xiii, 641 pages) : illustrations
Item Number
10.1007/978-3-031-07761-6 doi
Call Number
QC174.17.M35
Dewey Decimal Classification
530.1201/5118
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed November 1, 2022).
Available in Other Form
Print version: 9783031077609
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Chapter 1: The Basic Concepts
Part I: Single-Channel Problems
Chapter 2: SchrOdinger Equation and its Solutions
Chapter 3: Riemann Surface and the Spectral Points
Chapter 4: Scattering States and the S-Matrix
Chapter 5: Complex Angular Momentum
Chapter 6: Greens Functions
Chapter 7: Short-Range Potential Extending to Infinity
Chapter 8: Single-Channel Potential with Coulombic Tail
Part II: Multi-Channel Problems
Chapter 9: Non-Central Potential
Chapter 10: Systems with Non-Zero Spin
Chapter 11: Multi-Channel Schr Odinger Equation
Chapter 12: Multi-Channel Jost Matrix
Chapter 13: Riemann Surfaces for Multi-Channel Systems
Chapter 14: Multi-Channel Problems of Charged Particles
Chapter 15: Effective-Range Expansion and its Generalizations
Part III: Special Issues
Chapter 16: Singular and Low-Dimensional Potentials
Chapter 17: Miscellaneous Extensions of the Jost Function Approach
Chapter 18: Some Exactly Solvable Potential Models
Appendices
References and Index.

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