The Schrödinger and Riccati Equations

Softcover Nachdruck of the original 1. Auflage 1999
ISBN: 978-3-540-65105-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 70, 218 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 371 g

Reihe: Lecture Notes in Chemistry

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.

Zielgruppe

Research

Autoren/Hrsg.

Fraga, Serafin

Fraga, Eric S.

Garcia de la Vega, Jose M.

Inhaltsverzeichnis

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.