Hypervirial Theorems

A.- I. Hypervirial Theorems and Exact Solutions of the Schrödinger Equation.- II. Hypervirial Theorems and Perturbation Theory.- III. Hypervirial Theorems and the Variational Theorem.- IV. Non Diagonal Hypervirial Theorems and Approximate Functions.- V. Hypervirial Functions and Self-Consistent Field Functions.- VI. Perturbation Theory Without Wave Function.- B.- VII. Importance of the Different Boundary Conditions.- VIII. Hypervirial Theorems for 1D Finite Systems. General Boundary Conditions.- IX. Hypervirial Theorems for 1D Finite Systems. Dirichlet Boundary Conditions.- X. Hypervirial Theorems for Finite 1D Systems. Von Neumann Boundary Conditions.- XI. Hypervirial Theorems for Finite Multidimensional Systems.- Special Topics.- 46. Hypervirial theorems and statistical quantum mechanics.- 47. Hypervirial theorems and semiclassica1 approximation.- Numerical results.- References.- Appendix I. Evolution operators.- Appendix II. Hamiltonian of an isolated N-particles system.- Appendix III. Project ion operators.- Appendix IV. Perturbation theory.- Appendix V. Differentiation of matrices and determinants.- Apendix VI. Dynamics of systems with time independent Hamiltonians.- Appendix VII. Elements of probability theory for continuous random variables.- Appendix VIII. Electrons in crystal lattices.- Appendix IX. Numerical integration of the Schrödinger equation.- Appendix X. Expansion in cthz series and polynomial power coefficients.- Bibliography and References for Appendices.- Program I.- Program II.- Program III.- Program IV.- Program V.- Program VI.- Program VII.- Program VIII.- Program IX.- Program X.- Program XI.- Program XII.- Program XIII.- Program XIV.- Program XV.- Program XVI.- Program XVII.