Foundations and applications of variational and perturbation methods / S. Raj Vatsya.

Format:

Book

Author/Creator:

Vatsya, S. Raj.

Language:

English

Subjects (All):

Perturbation (Mathematics).

Perturbation (Quantum dynamics).

Variational principles.

Physical Description:

1 online resource (349 p.)

Edition:

1st ed.

Place of Publication:

Hauppauge, NY : Nova Science Publishers, c2009.

Language Note:

English

Summary:

Contents: Preface; Integration and vector spaces; Operators in vector spaces; Variational methods; Perturbation methods; Matrices; Atomic systems; Supplementary examples; References; Index.

Contents:

Intro

FOUNDATIONS AND APPLICATIONS OFVARIATIONAL AND PERTURBATIONMETHODS

CONTENTS

PREFACE

ACKNOWLEDGEMENTS

I. FOUNDATIONS

1. INTEGRATION AND VECTOR SPACES

1. I. PRELIMINARIES

1. II. INTEGRATION

1.II.1. Basic Concepts

1.II.2. Integration over Trajectories

1. III. VECTOR SPACES

2. OPERATORS IN VECTOR SPACES

2.I. OPERATORS IN BANACH SPACES

2.II. Operators in Hilbert Spaces

2.III. Forms in Hilbert Spaces

2.IV. Integral Transforms

2.V. Differential Operators

3. VARIATIONAL METHODS

3.I. FORMULATION

3.II. CONVERGENCE

3.II.1. Basic Results

3.II.2. Compact Operators

3.II.3. Bounded Operators

3.II.4. Semi-Bounded Operators

3.III. PADÉ APPROXIMANTS

3.III.1. Formulation

3.III.2. Representations

3.III.3. Convergence And Applications

3.IV. MONOTONIC CONVERGENCE

3.IV.1. Diagonal Forms

3.IV.2. Eigenvalues

4. PERTURBATION METHODS

4.I. PERTURBED OPERATOR

4.II. SPECTRAL PERTURBATION

4.II.1. Resolvent and Point Spectrum

4.II.2. Continuous Spectrum

4.III. SPECTRAL DIFFERENTIATION

4.IV. ITERATION

II. APPLICATIONS

5. MATRICES

5.I. TRIDIAGONAL MATRICES

5.II. STRUCTURED MATRICES

6. ATOMIC SYSTEMS

6.I. PRELIMINARIES

6.II. EIGENVALUES AND CRITICAL POINTS

6.II.1. Helium Atom

6.II.2. Short Range Potentials

6.III. SCATTERING

6.III.1. Formulation

6.III.2. Born Series

6.III.3. Schwinger's Method

6.III.4. Hulthén -Kohn Methods

6.III.5. Rotated Hamiltonians

7. SUPPLEMENTARY EXAMPLES

7.I. RAY TOMOGRAPHY

7.II. MAXWELL'S EQUATIONS

7.III. POSITIVITY LEMMA FOR THE ELLIPTIC OPERATORS

7.III.1. Basic Results

7.III.2. Applications

7.IV. TRANSPORT AND PROPAGATION

7.IV.1. Reaction-Diffusion

7.IV.2. Heat Transfer.

7.IV.3. Radiative Transfer

7.IV.4. Turbulent Diffusion

7.IV.5. Optical Beam Propagation

7.V. QUANTUM THEORY

REFERENCES

INDEX.

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [327]-330) and index.

ISBN:

1-60741-414-7