Introduction to Perturbation Theory in Quantum Mechanics

ISBN-13: 9780849318771 / Angielski / Twarda / 2000 / 288 str.

Francisco M. Fernandez; F. M. Fernandez

Opis

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.

Recenzje

"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

Spis treści

PERTURBATION THEORY IN QUANTUM MECHANICSBound StatesEquations of MotionExamplesPERTURBATION THEORY IN THE COORDINATE REPRESENTATIONThe Method of Dalgarno and StewartLogarithmic Perturbation TheoryThe Method of Fernandez and CastroPERTURBATION THEORIES WITHOUT WAVEFUNCTIONHypervirial and Hellmann-Feynman TheoremsThe Method of Swenson and DanforthMoment MethodPerturbation Theory in Operator FormSIMPLE ATOMIC AND MOLECULAR SYSTEMSThe Stark Effect in HydrogenThe Zeeman Effect in HydrogenThe Hydrogen Molecular IonThe Delta Molecular IonTHE SCHRODINGER EQUATION ON BOUNDED DOMAINSOne-Dimensional Box ModelsSpherical-Box ModelsPerturbed Rigid RotorsCONVERGENCE OF THE PERTURBATION SERIESConvergence Properties of Power SeriesRadius of Convergence of the Perturbation ExpansionsDivergent Perturbation SeriesImproving the Convergence Properties of the Perturbation SeriesPOLYNOMIAL APPROXIMATIONSOne-Dimensional ModelsCentral-Field ModelsVibration-Rotational Spectra of Diatomic MoleculesLarge-N ExpansionImproved Perturbation SeriesBorn-Oppenheimer Perturbation TheoryPERTURBATION THEORY FOR SCATTERING STATES IN ONE DIMENSIONOn the Solutions of Second-Order Differential EquationsThe One-Dimensional Schrödinger Equation with a Finite Interaction RegionThe Born ApproximationAn Exactly Solvable Model: The Square BarrierNontrivial Simple ModelsPerturbation Theory for Resonance TunnelingPERTURBATION THEORY IN CLASSICAL MECHANICSDimensionless Classical EquationsPolynomial ApproximationCanonical Transformations in Operator FormThe Evolution OperatorSecular Perturbation TheoryCanonical Perturbation TheoryThe Hypervirial Hellmann-Feynman Method (HHFM)Central ForcesMAPLE PROGRAMSAPPENDICESLaplacian in Curvilinear CoordinatesOrdinary Differential Equations with Constant CoefficientsCanonical TransformationsREFERENCES

O autorze

Francisco M. Fernandez