Large Order Perturbation Theory and Summation Methods in Quantum Mechanics [Paperback]

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.- 1. Some Fundamental Properties.- 2. The Hellmann-Feynman Theorem.- 3. Hypervirial Relations and General Boundary Conditions.- References Chapter I.- II. The Semiclassical Approximation and the JWKB Method.- 4. Adiabatic Invariants.- 5. Bohr-Sommerfeld Quantization Condition and JWKB Method.- 6. Applications of the JWKB Method.- References Chapter II.- III. Rayleigh-Schr?dinger Perturbation Theory (RSPT).- 7. The Rayleigh-Schr?dinger Perturbation Theory.- 8. Hypervirial Method to Generate the Perturbation Expansion.- 9. Other Methods to Generate the Perturbation Expansion.- References Chapter III.- IV. Divergence of the Perturbation Series.- 10. Divergence of the perturbation series.- 11. Mathematical Methods to study the Asymptotic Behaviour of the RS coefficients.- References of Chapter IV.- V. Perturbation Series Summation Techniques.- 12. Introduction to the summability of divergent or slowly convergent series.- 13. Pad? Approximants.- 14. Borel transform and Borel-Pad? summation method.- 15. Euler Summation Method.- 16. Perturbation series renormalization techniques.- 17. Wick ordering and perturbation series summation.- 18. Summation of perturbation series through orderdependent mappings.- References Chapter V.- VI. Foundations of the Variational Functional Method (VFM).- 19. Energy of parameter-dependent systems.- 20. Semiclassical functional expressions for the energy.- 21. Scaling Variational Method.- 22. VFM from Heisenberg inequalities.- References Chapter VI.- VII. Application of the VFM to One-Dimensional Systems with Trivial Boundary Conditions.- 23. Anharmonic oscillatorslÃ<