§16§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. §04§1 Introduction.- The Linear Schrödinger Equation.- 2 Derivation of the Schrödinger Equation.- 3 The Schrödinger Equation in Position Space.- 4 The Schrödinger Equation In Momentum Space.- 5 The Local Schrödinger Equation.- 6 The Time-Dependent Schrödinger Equation.- The Non-Linear Schrödinger Equation.- 7 The Non-Linear Schrödinger Equation.- The Riccati Equation.- 8 The Riccati Equation and Its Solution.- 9 Quantum-Mechanical Applications of the Riccati Equation.- The Schrödinger-Riccati Equation.- 10 The Schrödinger-Riccati Equation.- 11 Numerical Experience with the Schrödinger-Riccati Equation.- 12 References and Bibliography.- Appendix. Matrix Notation.
