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.

A

I. General Properties of the Eigenvalue Spectrum
II. The Semiclassical Approximation and the JWKB Method
III. Rayleigh-Schrödinger Perturbation Theory (RSPT)
IV. Divergence of the Perturbation Series
V. Perturbation Series Summation Techniques
VI. Foundations of the Variational Functional Method (VFM)
VII. Application of the VFM to One-Dimensional Systems with Trivial Boundary Conditions
VIII Application of the VFM to One-Dimensional Systems with Boundary Conditions for Finite Values of the Coordinates
IX Multidimensional Systems: The Problem of the Zeeman Effect in Hydrogen
X Application of the VFM to the Zeeman Effect in Hydrogen
XI Combination of VFM with RSPT: Application to Anharmonic Oscillators
XII Geometrical Connection between the VFM and the JWKB Method
B
XIII Generalization of the Functional Method as a Summation Technique of Perturbation Series
XIV Properties of the FM: Series with Non-Zero Convergence Radii
XV Properties of the FM: Series with Zero Convergence Radii
XVI Appication of the FM to the Anharmonic Oscillator
XVII Application of the FM to Models with Confining Potentials
XVIII Application of the FM to the Zeeman Effect in Hydrogen
XIX Application of the FM to the Stark Effect in Hydrogen
XX FM and Vibrational Potentials of Diatomic Molecules
Appendix A Scaling Laws of Schrödinger Operators
Appendix B Applications of the Anharmonic Oscillator Model
Appendix D Calculation of Integrals by the Saddle-Point Method
Appendix E Construction of Padé Approximants
Appendix F Normal Ordering of Operators
Appendix G Applications of Models with Confining Potentials
Appendix H Hamiltonian of an Hydrogen Atom in a Magnetic Field
Appendix I Asymptotic Behavior of the Binding Energy for the ZeemanEffect in the Hydrogen Atom
Appendix L RKR Method to Obtain Vibrational Potentials of Diatomic Molecules
References Appendices A-L.