Understanding the Schrödinger Equation

Some [Non]Linear Perspectives

Valentino A. Simpao (Herausgeber)

Buch | Hardcover

328 Seiten

2020
Nova Science Publishers Inc (Verlag)
978-1-5361-7662-9 (ISBN)

Infos

The current offering from Nova Science Publishers titled Understanding the Schrödinger 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 Schrödingers wavefunction formalism. The work is dedicated to providing an illustrative sketch of a few of the numerous and sundry aspects of the Schrödinger 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 Schrödinger 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 Schrödinger equation as an extension of probability theory. A chapter addressing the Schrödinger 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 Schrödinger 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 Schrödinger-like equation describing a cosmogonical body formation. A chapter addressing the nonlinear Schrödinger 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 Schrödinger equation. A chapter which puts forth a novel paradigm of infinite dimensional quantum phase space extension of the Schrödinger equation. A chapter which discusses a metaplectic Bohmian formalism from classical (Hamiltons equations) to quantum physics (Schrödingers 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 Schrödinger equation.

Inhalt

Preface; Acknowledgements; Understanding the Schrödinger Equation as a Kinematic Statement: A Probability-First Approach to Quantum; The Schrödinger Equation Written in the Second Quantization Formalism: Derivation from First Principles; Schrödinger Equation and Nonlinear Waves; On the Wave Solutions of the Generalized Nonlinear Schrödinger-Like Equation of Formation of a Cosmogonical Body; The Nonlinear Schrödinger Equation: A Mathematical Model with Its Wide Range of Applications; Self-Similar and Traveling-Wave Analysis of the Madelung Equations Obtained from the Schrödinger Equation; Paradigm of Infinite Dimensional Phase Space; From Classical to Quantum Physics: The Metatron; About the Editors; Index.

Produkt-Details

• Erscheinungsdatum: 06.07.2020
• Verlagsort: New York
• Sprache: englisch
• Gewicht: 576 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 1-5361-7662-1 / 1536176621
• ISBN-13: 978-1-5361-7662-9 / 9781536176629
• Zustand: Neuware