Hypervirial Theorems [Paperback]

A.- I. Hypervirial Theorems and Exact Solutions of the Schr?dinger Equation.- 1. Equations of motion.- 2. Diagonal hypervirial theorems.- 3. Off-diagonal hypervirial theorems.- 4. Quantum-mechanical sum rules.- 5. Recurrence relations among matrix elements of functions of the coordinate.- 6. Hypervirial theorems for unbound states.- 7. Quantum-mechanical virial theorem.- 8. Derivatives of the energy with respect to a parameter in the Hamiltonian operator.- References Chapter I.- II. Hypervirial Theorems and Perturbation Theory.- 9. Ray1eigh-Schr?dinger perturbation theory.- 10. Perturbation theory and hypervirial theorems.- References Chapter II.- III. Hypervirial Theorems and the Variational Theorem.- 11. Variational theorem.- 12. Unitary operator formalism.- 13. Point transformation formalism.- 14. Hellmann-Feynman theorem and variational functions.- 15. Simultaneous hypervirial relationships.- 16. Hypervirial relations and symmetry conditions.- 17. Tensorial generalization of the quantum virial theorem.- 18. Coordinate shifting (Translation).- 19. Some worked examples illustrating the application of the several transformations.- 20. Linear transformation and correlation of variables.- Numerical results.- References Chapter III.- IV. Non Diagonal Hypervirial Theorems and Approximate Functions.- 21. Fundamental theorems.- 22. The non diagona1-diagona1 hypervirlal iterative method.- 23. Sum rules and approximate functions.- 24. Non diagonal hypervirial theorems and approximate functions.- 25. Hypervirial theorems and orthogonality conditions.- 26. Restricted variational method.- References Chapter IV.- V. Hypervirial Functions and Self-Consistent Field Functions.- 27. Self-consistent functions. Hartree Method.- 28. Self-consistent function for identical particles. Hartree-Fock Method.- Numerical results.- References Chapter V.- VI. Perturbation Theory Without Wave Function.- 29. 1D Models.- 30. Central potential systems.- 31. 1D systems with periodic potentials.- NulÓ$