Introduction to Perturbation Theory in Quantum Mechanics

PERTURBATION THEORY IN QUANTUM MECHANICS Bound States Equations of Motion Examples PERTURBATION THEORY IN THE COORDINATE REPRESENTATION The Method of Dalgarno and Stewart Logarithmic Perturbation Theory The Method of Fernandez and Castro PERTURBATION THEORIES WITHOUT WAVEFUNCTION Hypervirial and Hellmann-Feynman Theorems The Method of Swenson and Danforth Moment Method Perturbation Theory in Operator Form SIMPLE ATOMIC AND MOLECULAR SYSTEMS The Stark Effect in Hydrogen The Zeeman Effect in Hydrogen The Hydrogen Molecular Ion The Delta Molecular Ion THE SCHRODINGER EQUATION ON BOUNDED DOMAINS One-Dimensional Box Models Spherical-Box Models Perturbed Rigid Rotors CONVERGENCE OF THE PERTURBATION SERIES Convergence Properties of Power Series Radius of Convergence of the Perturbation Expansions Divergent Perturbation Series Improving the Convergence Properties of the Perturbation Series POLYNOMIAL APPROXIMATIONS One-Dimensional Models Central-Field Models Vibration-Rotational Spectra of Diatomic Molecules Large-N Expansion Improved Perturbation Series Born-Oppenheimer Perturbation Theory PERTURBATION THEORY FOR SCATTERING STATES IN ONE DIMENSION On the Solutions of Second-Order Differential Equations The One-Dimensional Schroedinger Equation with a Finite Interaction Region The Born Approximation An Exactly Solvable Model: The Square Barrier Nontrivial Simple Models Perturbation Theory for Resonance Tunneling PERTURBATION THEORY IN CLASSICAL MECHANICS Dimensionless Classical Equations Polynomial Approximation Canonical Transformations in Operator Form The Evolution Operator Secular Perturbation Theory Canonical Perturbation Theory The Hypervirial Hellmann-Feynman Method (HHFM) Central Forces MAPLE PROGRAMS APPENDICES Laplacian in Curvilinear Coordinates Ordinary Differential Equations with Constant Coefficients Canonical Transformations REFERENCES