Meet the editor

Paul Bracken, PhD, is a professor in the Department of Mathematics at the University of Texas, Edinburg. He received a BSc from the University of Toronto and a PhD from the University of Waterloo in Canada. His research interests include applications of differential geometry and partial differential equations to problems in mathematical physics, such as gravity, as well as problems in quantum mechanics and quantum field theory. He

has published more than 160 papers in journals and books and presented talks at numerous meetings and conferences. This is the sixth volume he has contributed with IntechOpen.

Contents

**Section 1**

Problem

**Section 2**

Structure Interactions

*and Marimuthu Karunakaran*

*by María Esther Burgos*

Uncertainty Relations *by Kenjiro Yanagi*

to Quantum Mechanics

*by Vahram Mekhitarian*

*by Paul Bracken*

*by Ciann-Dong Yang and Shiang-Yi Han*

to Nonequilibrium Thermodynamics

Entropy in Quantum Mechanics and Applications

*by Betül Çalişkan and Ali Cengiz Çalişkan*

Exactly Solvable Problems in Quantum Mechanics

**Preface XI**

Solvable Systems **1**

**Chapter 1 3**

**Chapter 2 13**

**Chapter 3 31**

Foundational Problems in Quantum Mechanics **45**

**Chapter 4 47**

**Chapter 5 65**

**Chapter 6 83**

**Chapter 7 107**

Dipolar Interactions: Hyperfine Structure Interaction and Fine

*by Lourdhu Bruno Chandrasekar, Kanagasabapathi Gnanasekar*

Transitions between Stationary States and the Measurement

Complex Space Nature of the Quantum World: Return Causality

Equations of Relativistic and Quantum Mechanics (without Spin)

## Contents



Preface

Quantum mechanics has been remarkably successful at accounting for physical phenomena at very small scales. The area of quantum mechanics has become a fundamental part of modern physics and hence a very intensive subject for

quantum Hall effect.

mechanics.

tum mechanics have become very widespread.

research. It is applicable to physical situations where matter can be studied on very small scales from atoms and molecules to physics of the solid state and elementary particles. It has also generated new areas of physics in its wake that require quantum mechanics for their understanding, such as Bose Einstein condensation and the

This book presents 12 solid contributions that illustrate the range and diversity of topics in quantum mechanics. Of these 12 chapters, three reference solvable models such as hyperfine structure interactions. Other chapters cover some foundational issues such as complex space forms of quantum mechanics, entropy in quantum mechanics, and equations of relativistic quantum mechanics. The final chapters examine applications of quantum mechanics to more complicated situations. As illustrated by this book, the scope, influence, and domain of applicability of quan-

This book is a result of the hard work of an international group of invited authors. It is a pleasure to thank them for their efforts and scientific contributions. I am grateful to acknowledge with many thanks the assistance of Mr Mateo Pulko who was the publishing coordinator and manager throughout the production process of this book. It is also a pleasure to thank IntechOpen for the opportunity to work on this volume, which serves to further study the fascinating subject of quantum

> **Paul Bracken** Professor,

> > USA

University of Texas,

Department of Mathematics,
