Introduction to Perturbation Theory in Quantum Mechanics: 1st Edition (Hardback) book cover

Introduction to Perturbation Theory in Quantum Mechanics

1st Edition

By Francisco M. Fernandez

CRC Press

288 pages

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Hardback: 9780849318771
pub: 2000-09-19
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Description

Perturbation theory is a powerful tool for solving a wide variety of problems in applied mathematics, a tool particularly useful in quantum mechanics and chemistry. Although most books on these subjects include a section offering an overview of perturbation theory, few, if any, take a practical approach that addresses its actual implementation

Introduction to Perturbation Theory in Quantum Mechanics does. It collects into a single source most of the techniques for applying the theory to the solution of particular problems. Concentrating on problems that allow exact analytical solutions of the perturbation equations, the book resorts to numerical results only when necessary to illustrate and complement important features of the theory. The author also compares different methods by applying them to the same models so that readers clearly understand why one technique may be preferred over another.

Demonstrating the application of similar techniques in quantum and classical mechanics, Introduction to Perturbation Theory in Quantum Mechanics reveals the underlying mathematics in seemingly different problems. It includes many illustrative examples that facilitate the understanding of theoretical concepts, and provides a source of ideas for many original research projects.

Reviews

"Professor Fernandez [has been] active in the field of quantum mechanical perturbation theory for many years. … [T]he book has been prepared and written with-and to-the author's undisguised delight, offering a specific blend of the theory and computations. … The book informs the reader, in an admirably compact and still unbelievably digestible text, about virtually all the basic concepts … ."

- Zentralblatt MATH, Vol. 1048

"… summarizes in detail a wide variety of techniques used in perturbation theory that were developed for particular problems. To make the methods easily comparable, they are applied to the same models. Some of these models have exact solutions, so that improvement in the perturbation series and their limitations become clear…author intentionally avoids problems that require numerical computation and tries to keep the mathematics as simple as possible in order to concentrate the reader's attention on the ideas underlying each method…offers an invaluable source of ideas for theoreticians applying perturbation methods to various problems in chemistry and physics…it can also be used for teaching undergraduate and graduate courses…"

-Journal of the American Chemical Society, Vol. 123, No. 26

"…a very substantial presentation of perturbation theory in quantum mechanics, much of which is based on the publication of the author and his coworkers…the book is clearly an important reference work in the field, and the author has completed a laudable task."

-Mathematical Reviews, Issue 2002

Table of Contents

PERTURBATION THEORY IN QUANTUM MECHANICS

Bound States

Equations of Motion

Examples

PERTURBATION THEORY IN THE COORDINATE REPRESENTATION

The Method of Dalgarno and Stewart

Logarithmic Perturbation Theory

The Method of Fernandez and Castro

PERTURBATION THEORIES WITHOUT WAVEFUNCTION

Hypervirial and Hellmann-Feynman Theorems

The Method of Swenson and Danforth

Moment Method

Perturbation Theory in Operator Form

SIMPLE ATOMIC AND MOLECULAR SYSTEMS

The Stark Effect in Hydrogen

The Zeeman Effect in Hydrogen

The Hydrogen Molecular Ion

The Delta Molecular Ion

THE SCHRODINGER EQUATION ON BOUNDED DOMAINS

One-Dimensional Box Models

Spherical-Box Models

Perturbed Rigid Rotors

CONVERGENCE OF THE PERTURBATION SERIES

Convergence Properties of Power Series

Radius of Convergence of the Perturbation Expansions

Divergent Perturbation Series

Improving the Convergence Properties of the Perturbation Series

POLYNOMIAL APPROXIMATIONS

One-Dimensional Models

Central-Field Models

Vibration-Rotational Spectra of Diatomic Molecules

Large-N Expansion

Improved Perturbation Series

Born-Oppenheimer Perturbation Theory

PERTURBATION THEORY FOR SCATTERING STATES IN ONE DIMENSION

On the Solutions of Second-Order Differential Equations

The One-Dimensional Schrödinger Equation with a Finite Interaction Region

The Born Approximation

An Exactly Solvable Model: The Square Barrier

Nontrivial Simple Models

Perturbation Theory for Resonance Tunneling

PERTURBATION THEORY IN CLASSICAL MECHANICS

Dimensionless Classical Equations

Polynomial Approximation

Canonical Transformations in Operator Form

The Evolution Operator

Secular Perturbation Theory

Canonical Perturbation Theory

The Hypervirial Hellmann-Feynman Method (HHFM)

Central Forces

MAPLE PROGRAMS

APPENDICES

Laplacian in Curvilinear Coordinates

Ordinary Differential Equations with Constant Coefficients

Canonical Transformations

REFERENCES

Subject Categories

BISAC Subject Codes/Headings:
SCI013050
SCIENCE / Chemistry / Physical & Theoretical
SCI040000
SCIENCE / Mathematical Physics
SCI057000
SCIENCE / Quantum Theory