Synopses & Reviews
The linear SchrAdinger equation is central to Quantum Chemistry. It is presented within the context of relativistic Quantum Mechanics and analysed both in time-dependent and time-independent forms. The Riccati equation is used to study the one-dimensional SchrAdinger equation.
The authors develop the SchrAdinger-Riccati equation as an approach to determine solutions of the time-independent, linear SchrAdinger equation.
Synopsis
The linear Schrödinger equation is central to Quantum Chemistry. It is presented within the context of relativistic Quantum Mechanics and analysed both in time-dependent and time-independent forms. The Riccati equation is used to study the one-dimensional Schrödinger equation. The authors develop the Schrödinger-Riccati equation as an approach to determine solutions of the time-independent, linear Schrödinger equation.
Synopsis
The linear Schrödinger equation is presented in the context of relativistic Quantum Mechanics. It is analysed in time-dependent and time-independent forms and its local and global properties are inspected. The authors develop the Schrödinger-Riccati equation as an approach to determine solutions of the time-independent, linear Schrödinger equation.
Table of Contents
Introduction.- Derivation of the Schrödinger Equation.- The Schrödinger Equation in Position Space.- The Schrödinger Equation in Momentum Space.- The Local Schrödinger Equation.- The Time-Dependent Schrödinger Equation.- The Non-Linear Schrödinger Equation.- The Riccati Equation and Its Solution.- Quantum-Mechanical Applications of the Riccati Equation.- The Schrödinger-Riccati Equation.- Numerical Experience with the Schrödinger-Riccati Equation.- References and Bibliography.- Appendix.- Matrix Notation.