Quantum Theory from a Nonlinear Perspective

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • Dieter Schuch

   Pages 1-8

3. Time-Dependent Schrödinger Equation and Gaussian Wave Packets

   • Dieter Schuch

   Pages 9-67

4. Time-Independent Schrödinger and Riccati Equations

   • Dieter Schuch

   Pages 69-83

5. Dissipative Systems with Irreversible Dynamics

   • Dieter Schuch

   Pages 85-131

6. Irreversible Dynamics and Dissipative Energetics of Gaussian Wave Packet Solutions

   • Dieter Schuch

   Pages 133-177

7. Dissipative Version of Time-Independent Nonlinear Quantum Mechanics

   • Dieter Schuch

   Pages 179-185

8. Nonlinear Riccati Equations in Other Fields of Physics

   • Dieter Schuch

   Pages 187-209

9. Summary, Conclusions and Perspectives

   • Dieter Schuch

   Pages 211-228

10. Back Matter

    Pages 229-258

    PDF

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.

• Complex Riccati Equations
• Connecting Nonlinear Dynamics and Quantum Mechanics
• Dissipation in Classical and Quantum Mechanics
• Ermakov Systems and Invariants
• Irreversibility in Classical and Quantum Mechanics
• Nonlinear Riccati Equations
• Nonlinearities in Quantum Mechanics
• ordinary differential equations

• Institut für Theoretische Physik, Goethe-University Frankfurt am Main, Frankfurt am Main, Germany

  Dieter Schuch

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-Universität Frankfurt am Main where he was also awarded his Habilitation for Theoretical Physics in 1992 and has been an Apl.-Professor since 2002. Guest Professorships and collaborations took him to IBM, New York, Toronto, Canada, Auckland, New Zealand, Nice, France, UNAM and CINVESTAV, Mexico, Granada, Spain, Salerno, Italy and the Frankfurt Institute for Advanced Studies (FIAS). Since 2009, he has undertaken the organization of the international conference series “Symmetries in Science”.

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