Quantum Theory from a Nonlinear Perspective: Riccati Equations in Fundamental Physics [Hardcover]

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.Introduction.- Time-Dependent Schr?dinger Equation and Gaussian Wave Packets.- Time-Independent Schr?dinger Equation and Riccati Equations.- Dissipative Systems with Irreversible Dynamics.- Irreversible Dynamics and Dissipative Energetics of Gaussian Wave Packet Solutions.- Dissipative Version of Time-Independent Nonlinear Quantum Mechanics.- Nonlinear Riccati Equations in Other Fields of Physics.- Summary, Conclusions and Outlook.Prof. Dr. Dieter Schuch
Institut fuer Theoretische Physik
Goethe-Universitaet Frankfurt am Main
Max-von-Laue-Str. 1
D-60438 Frankfurt am Main, Germany

Dieter Schuch received his Dr. Phil. nat. (1982) for Theoretical and Physical Chemistry at the J.W. Goethe-Universit?t Frankfurt am Main where he was also awarded his Habilitation for Theoretical Physics in 1992 and has been an Apl.-Professor since 2002. Guest ProfessorshipslS'