Algebraic Methods in Quantum Chemistry and Physics

ISBN: 9780849382925 出版年：2020 页码：280 Fernandez, Francisco M Castro, E A CRC Press

ELEMENTARY INTRODUCTION TO LIE ALGEBRAS AND OPERATOR METHODS Vector Spaces Lie Algebras Superoperators Canonical Transformations Operator Differential Equations The Campbell-Baker-Hausdorff Formula Basis Set for a Lie Algebra SOME PRACTICAL APPLICATIONS OF FINITE-DIMENSIONAL LIE ALGEBRAS Definition, Examples, and Some Applications of Finite-Dimensional Lie Algebras Regular or Adjoint Matrix Representation Eigenvalues of Superoperators Faithful Matrix Representation Disentangling Exponential Operators THE QUANTUM-MECHANICAL HARMONIC OSCILLATOR Eigenvalues, Eigenvectors, and Matrix Elements Coherent States The Coordinate Representation Modeling Quantum-Mechanical Systems with Bosonic Algebra MATRIX ELEMENTS OF EXPONENTIAL OPERATORS IN THE HARMONIC OSCILLATOR BASIS SET Matrix Elements of Exponential Operators Franck-Condon Factors THREE-DIMENSIONAL LIE ALGEBRAS AND SOME OF THEIR REALIZATIONS IN QUANTUM MECHANICS Eigenvalues and Matrix Elements Angular Momentum and Bosonic Algebras Second-Order Differential Operators Exactly Solvable Models with Central Potentials The Method of Canonical Transformations Examples in Quantum Mechanics Selection Rules PERTURBATION THEORY AND VARIATIONAL METHOD Perturbation Theory for Stationary States The Vibration-Rotational Spectrum of a Diatomic Molecule Perturbation Theory in Operator Form Perturbation Theory and Canonical Transformations Lie Algebras and the Variational Method NUMERICAL INTEGRATION OF THE TIME-INDEPENDENT SCHRODINGER EQUATION Approximate Difference Equation The Propagation Matrix Method An Exactly Solvable Problem Propagation on a Grid Perturbative Solutions Exponential Solution Product of Exponentials EQUATIONS OF MOTION IN QUANTUM MECHANICS Schrodinger, Heisenberg, and Intermediate Pictures Approximate Methods The Density Operator Finite-Dimensional Lie Algebras and Observables BILINEAR OSCILLATORS General Bilinear Oscillator for One Degree of Freedom Exactly Solvable Example Transition Probabilities for a General Bilinear Oscillator Solution to the Schrodinger Equation in the Coordinate Representation Pseudo-Nonlinear Hamiltonians Fokker-Planck Equation Bilinear Approximation to Arbitrary Potential Energy Functions PARAMETERIZATION OF THE TIME-EVOLUTION OPERATOR The Magnus Expansion and Perturbation Theory Simple Bilinear Hamiltonians State Space of Finite Dimension Product of Exponential Operators SEMICLASSICAL EXPANSIONS IN STATISTICAL MECHANICS The Canonical Ensemble The Wigner-Kirkwood Expansion The Harmonic Oscillator The Euler-MacLaurin Summation Formula The Poisson Summation Formula NOTE: Introduction at the beginning of each chapter