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

Description

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. Front Matter ....Pages i-xiv Introduction (Dieter Schuch)....Pages 1-8 Time-Dependent Schrödinger Equation and Gaussian Wave Packets (Dieter Schuch)....Pages 9-67 Time-Independent Schrödinger and Riccati Equations (Dieter Schuch)....Pages 69-83 Dissipative Systems with Irreversible Dynamics (Dieter Schuch)....Pages 85-131 Irreversible Dynamics and Dissipative Energetics of Gaussian Wave Packet Solutions (Dieter Schuch)....Pages 133-177 Dissipative Version of Time-Independent Nonlinear Quantum Mechanics (Dieter Schuch)....Pages 179-185 Nonlinear Riccati Equations in Other Fields of Physics (Dieter Schuch)....Pages 187-209 Summary, Conclusions and Perspectives (Dieter Schuch)....Pages 211-228 Back Matter ....Pages 229-258