**Meet the editor**

The editor Dr. Paul Bracken is a Professor currently a Professor in the Mathematics Department at the University of Texas in Edinburg, TX. He obtained his BSc degree from the University of Toronto and PhD degree from the University of Waterloo in Canada. His research interests include mathematical problems in quantum mechanics and quantum field theory, differential geom-

etry and partial differential equations as well as gravity. He has published over one hundred papers in journals and books and as well presented about twenty talks at various meetings and conferences and have taught courses at all levels over the years.

Contents

**Preface IX**

**Section 1 The Classical-Quantum Correspondence 1**

**Between Conjugate Variables 3**

Gabino Torres-Vega

**Kepler Problem 23**

Francisco De Zela

**Section 2 The Schrödinger Equation 79**

**Decoherence 81**

Kazuyuki Fujii

Shimada

Sanchez

Chapter 1 **Classical and Quantum Conjugate Dynamics – The Interplay**

Keita Sumiya, Hisakazu Uchiyama, Kazuhiro Kubo and Tokuzo

**Possible Bridge Between Classical and Quantum Physics 41**

**Nonlinearity, Dynamical Scalar Product and some Ideas of**

Chapter 3 **Charathéodory's "Royal Road" to the Calculus of Variations: A**

Chapter 4 **The Improvement of the Heisenberg Uncertainty Principle 67** L. M. Arévalo Aguilar, C. P. García Quijas and Carlos Robledo-

Chapter 5 **Schrödinger Equation as a Hamiltonian System, Essential**

Chapter 6 **Schrödinger Equation and (Future) Quantum Physics 105** Miloš V. Lokajíček, Vojtěch Kundrát and Jiří Procházka

Jan J. Sławianowski and Vasyl Kovalchuk

Chapter 7 **Quantum Damped Harmonic Oscillator 133**

Chapter 2 **Classical and Quantum Correspondence in Anisotropic**
