Contents

#### **Preface XIII**


#### **X** Contents

#### **Section 3 Path Integrals 157**


Chapter 17 **On the Dual Concepts of 'Quantum State' and 'Quantum**

Contents **VII**

Chapter 18 **The Computational Unified Field Theory (CUFT): A Candidate**

Chapter 20 **The Wigner-Heisenberg Algebra in Quantum Mechanics 477**

**Quantum Mechanics for Bound State Calculations 499** Chia-Chun Chou, Mason T. Biamonte, Bernhard G. Bodmann and

Chapter 21 **New System-Specific Coherent States by Supersymmetric**

**Process' 371**

Cynthia Kolb Whitney

Jonathan Bentwich

John P. Ralston

Donald J. Kouri

Chapter 22 **Quantum Dating Market 521**

Peter Enders

**and Cloning 565** GianCarlo Ghirardi

**in Nanosystems 623** M. D. Bal'makov

**'Theory of Everything' 395**

Chapter 19 **Emergent un-Quantum Mechanics 437**

Rafael de Lima Rodrigues

**Section 6 Quantization and Entanglement 519**

Chapter 23 **Quantization as Selection Rather than Eigenvalue Problem 543**

C. M. Arizmendi and O. G. Zabaleta

Chapter 24 **Entanglement, Nonlocality, Superluminal Signaling**

Sergio Curilef and Flavia Pennini

**Section 7 Quantum Information and Related Topics 621**

Chapter 25 **The Husimi Distribution: Development and Applications 595**

Chapter 26 **The Quantum Mechanics Aspect of Structural Transformations**


**Section 3 Path Integrals 157**

**VI** Contents

Paul Bracken

Valeriy I. Sbitnev

**Transforms 213** Francisco Bulnes

**Section 4 Perturbation Theory 245**

**Banach Spaces 247**

Yasuteru Shigeta

Inge S. Helland

A. Nicolaidis

Chapter 16 **Relational Quantum Mechanics 361**

S. M. Motevalli and M. Azimi

Chapter 14 **Unruh Radiation via WKB Method 317** Douglas A. Singleton

**Section 5 Foundations of Quantum Mechanics 333**

Chapter 15 **A Basis for Statistical Theory and Quantum Theory 335**

Chapter 13 **Quantal Cumulant Mechanics as Extended Ehrenfest Theorem 293**

Chapter 8 **The Schwinger Action Principle and Its Applications to**

Chapter 9 **Generalized Path Integral Technique: Nanoparticles Incident on a Slit Grating, Matter Wave Interference 183**

Chapter 10 **Quantum Intentionality and Determination of Realities in the Space-Time Through Path Integrals and Their Integral**

Chapter 11 **Convergence of the Neumann Series for the Schrödinger Equation and General Volterra Equations in**

Fernando D. Mera and Stephen A. Fulling

Chapter 12 **Quantum Perturbation Theory in Fluid Mixtures 269**

**Quantum Mechanics 159**


Preface

It can be stated that one of the greatest creations of twentieth century physics has been quan‐ tum mechanics. This has brought with it a revolutionary view of the physical world in its wake initiated by the work of people like Bohr, Schrödinger, Heisenberg and Born, Pauli and Dirac and many others. The development of quantum mechanics has taken physics in a vastly new direction from that of classical physics from the very start. This is clear from the compli‐ cated mathematical formalism of quantum mechanics and the intrinsic statistical nature of measurement theory. In fact, there continue at present to be many developments in the subject of a very fundamental nature, such as implications for the foundations of physics, physics of entanglement, geometric phases, gravity and cosmology and elementary particles as well. Quantum mechanics has had a great impact on technology and in applications to other fields such as chemistry and biology. The intention of the papers in this volume is to give research‐ ers in quantum mechanics, mathematical physics and mathematics an overview and introduc‐

Of the 29 chapters, the range of topics to be presented is limited to discussions on the founda‐ tions of quantum mechanics, the Schrödinger equation and quantum physics, the relationship of the classical-quantum correspondence, the impact of the path integral concept on quantum mechanics, perturbation theory, quantization and finally some informational-entropy aspects and application to biophysics. Many of the papers could be placed into more than one of these

The book has been put together by a large international group of invited authors and it is neces‐ sary to thank them for their hard work and contributions to the book. I gratefully acknowledge with thanks to the assistance provided by Ms. Danijela Duric who was publishing manager dur‐

> **Professor Paul Bracken** Department of Mathematics, University of Texas, Edinburg, TX

> > USA

ing the publishing process, and Intech publishing group for the publication of the book.

tion to some of the topics which are of current interest in this area.

sections, so their breadth is quite substantial.

