Understanding the Schrödinger equation : some (non) linear perspectives
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Bibliographic Information
Understanding the Schrödinger equation : some (non) linear perspectives
（Mathematics research developments series）
Nova Science Publishers, Inc., c2020
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Includes bibliographical references and index
Description and Table of Contents
Description
The current offering from Nova Science Publishers titled Understanding the Schroedinger Equation: Some [Non]Linear Perspectives is a collection of selectively invited manuscripts from some of the worlds leading workers in quantum dynamics; particularly as concerning Schroedingers wavefunction formalism. The work is dedicated to providing an illustrative sketch of a few of the numerous and sundry aspects of the Schroedinger equation; ranging from a new pedagogical teaching approach, to technical applications and foundational considerations. Towards this end, the work is generally of a theoretical nature; expounding various physical aspects of both linear and nonlinear Schroedinger systems and their attendant mathematical developments. Expressly, the book contains A chapter meant to give a new pedagogical paradigm for teaching an understanding of quantum mechanics, via the Schroedinger equation as an extension of probability theory. A chapter addressing the Schroedinger equation written in the second quantization formalism, derived from first principles; towards a deeper understanding of classical-quantum correspondence. A chapter discussing the connection between the Schroedinger equation and one of the most intuitive research fields in classical mechanics: the theory of nonlinear water waves. A chapter which investigates wave solutions of the generalized nonlinear time-dependent Schroedinger-like equation describing a cosmogonical body formation. A chapter addressing the nonlinear Schroedinger equation: a mathematical model with its wide-ranging applications and analytical results. A chapter investigating analytical self-similar and traveling-wave solutions of the Madelung equations obtained from the Schroedinger equation. A chapter which puts forth a novel paradigm of infinite dimensional quantum phase space extension of the Schroedinger equation. A chapter which discusses a metaplectic Bohmian formalism from classical (Hamiltons equations) to quantum physics (Schroedingers equation): the Metatron. The book is written in a lucid style, nicely marrying physical intuition with mathematical insight. As such, it should be of interest to workers in Schrodinger theory and related areas, and generally, to those who seek a deeper understanding of some of the linear and nonlinear perspectives of the Schroedinger equation.
Table of Contents
- Preface
- Acknowledgements
- Understanding the Schroedinger Equation as a Kinematic Statement: A Probability-First Approach to Quantum
- The Schroedinger Equation Written in the Second Quantization Formalism: Derivation from First Principles
- Schroedinger Equation and Nonlinear Waves
- On the Wave Solutions of the Generalized Nonlinear Schroedinger-Like Equation of Formation of a Cosmogonical Body
- The Nonlinear Schroedinger Equation: A Mathematical Model with Its Wide Range of Applications
- Self-Similar and Traveling-Wave Analysis of the Madelung Equations Obtained from the Schroedinger Equation
- Paradigm of Infinite Dimensional Phase Space
- From Classical to Quantum Physics: The Metatron
- About the Editors
- Index.
by "Nielsen BookData"