Large Order Perturbation Theory and Summation Methods in Quantum Mechanics

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.