An introduction to inverse problems in physics / M Razavy, University of Alberta, Canada.

Format:

Book

Author/Creator:

Razavy, Mohsen, author.

Contributor:

World Scientific (Firm)

Emma Louise McClellan Fund.

Language:

English

Subjects (All):

Inverse problems (Differential equations).

Differential equations--Numerical solutions.

Differential equations.

Mathematical physics.

Physical Description:

1 online resource (xii, 374 pages) : illustrations (some color)

Place of Publication:

New Jersey : World Scientific, [2020]

System Details:

text file

Contents:

Intro

Contents

Preface

Introduction

References

1 Inverse Problems in Classical Dynamics

1.1 Inverse Problem for Trajectory

1.2 Determination of the Shape of the Potential Energy from the Period of Oscillation

1.3 Action Equivalent Hamiltonians

1.4 Abel's Original Inverse Problem

1.5 Inverse Scattering Problem in Classical Mechanics

1.6 Inverse Problem of a Linear Chain of Masses Coupled to Springs

1.7 Direct Problem of Non-exponential and of Exponential Decays in a Linear Chain

1.8 Inverse Problem of Dynamics for a Non-uniform Chain

1.9 Direct and Inverse Problems of Analytical Dynamics

1.10 From the Classical Equations of Motion to the Lagrangian and Hamiltonian Formulations

1.11 Langevin and Fokker-Planck Equations

2 Inverse Problems in Semiclassical Formulation of Quantum Mechanics

2.1 Quantum Mechanical Bound States for Confining Potentials

2.2 Semiclassical Formulation of the Inverse Scattering Problem

3 Inverse Problems and the Heisenberg Equations of Motion

3.1 Equations of Motion Derived from the Hamiltonian Operator

3.2 Determination of the Commutation Relations From the Equations of Motion

3.3 Construction of the Hamiltonian Operator as an Inverse Problem

4 Inverse Scattering Problem for the Schrodinger Equation and the Gel'fand-Levitan Formulation

4.1 The Jost Solution

4.2 The Jost Function

4.3 The Levinson Theorem

4.4 The Gel'fand-Levitan Equation

4.5 Inverse Problem for One-dimensionalSchrodinger Equation

4.6 Bargmann Potentials

4.7 The Jost and Kohn Method of Inversion

5 Marchenko's Formulation of the Inverse Scattering Problem

5.1 Mathematical Preliminaries

5.2 Bound States Embedded in Continuum

5.3 More Solvable Potentials Found from Inverse Scattering

5.4 The Inverse Problem for Reflection and Transmission from a Barrier

5.5 A Special Problem in Electromagnetic Inverse Scattering

5.6 Construction of Reflectionless Potentials

5.7 Symmetric Reflectionless Potentials Supporting a Given Set of Bound States

6 Newton-Sabatier Approach to the Inverse Problem at Fixed Energy

6.1 Construction of the Potential at Fixed Energy

Notes:

Includes bibliographical references and index.

Electronic reproduction. Singapore Available via World Wide Web.

Description based on online resource; title from digital title page (viewed on July 13, 2020).

Local Notes:

Acquired for the Penn Libraries with assistance from the Emma Louise McClellan Fund.

Other Format:

Print version: Razavy, Mohsen. An introduction to inverse problems in physics

ISBN:

9789811221675

9811221677

Publisher Number:

99987262065

Access Restriction:

Restricted for use by site license.