Large Order Perturbation Theory and Summation Methods in Quantum Mechanics

✍ Scribed by G. A. Arteca, F. M. Fernández, E. A. Castro (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1990
• Tongue: English
• Leaves: 654
• Series: Lecture Notes in Chemistry 53
• Edition: 1
• Category: Library

✦ Synopsis

The book provides a general, broad approach to aspects of perturbation theory. The aim has been to cover all topics of interest, from construction, analysis, and summation of perturbation series to applications. Emphasis is placed on simple methods, as well as clear, intuitive ideas stemming from the physics of systems of interest.

✦ Table of Contents

Front Matter....Pages I-XI
Large Order Perturbation Theory and Summation Methods in Quantum Mechanics....Pages 1-4
General Properties of the Eigenvalue Spectrum....Pages 5-22
The Semiclassical Approximation and the JWKB Method....Pages 23-44
Rayleigh-Schrodinger Perturbation Theory (RSPT)....Pages 45-71
Divergence of the Perturbation Series....Pages 72-109
Perturbation Series Summation Techniques....Pages 110-140
Foundations of the Variational Functional Method (VFM)....Pages 141-164
Application of the VFM to One-Dimensional Systems with Trivial Boundary Conditions....Pages 165-189
Application of the VFM to One-Dimensional Systems with Boundary Conditions for Finite Values of the Coordinates....Pages 190-216
Multidimensional Systems: The Problem of the Zeeman Effect in Hydrogen....Pages 217-253
Application of the VFM to the Zeeman Effect in Hydrogen....Pages 254-271
Combination of VFM with RSPT: Application to Anharmonic Oscillators....Pages 272-304
Geometrical Connection Between the VFM and the JWKB Method....Pages 305-328
Front Matter....Pages 329-329
Properties of the FM: Series with Non-Zero Convergence RADII.....Pages 330-380
Properties of the FM: Series with Zero Convergence RADII....Pages 381-414
Application of the FM to the Anharmonic Oscillator....Pages 415-454
Application of the FM to Models with Confining Potentials....Pages 455-477
Application of the FM to the Zeeman Effect in Hydrogen....Pages 478-493
Application of the FM to the Stark Effect in Hydrogen....Pages 494-533
Front Matter....Pages 534-553
FM and Vibrational Potentials of Diatomic Molecules....Pages 329-329
Back Matter....Pages 554-580
....Pages 581-644

✦ Subjects

Theoretical and Computational Chemistry;Systems Theory, Control;Calculus of Variations and Optimal Control;Optimization;Math. Applications in Chemistry;Computational Intelligence;Quantum Physics