**Meet the editor**

Dr Mohammad Reza Pahlavani, was born in 1958 at north-east of Iran. He has been obtained his Bs.c from Mashhad University (Mashhad-Iran), Ms.c from Tehran University (Tehran-Iran) and Ph.D from Indian Institute of technology Bombay (Mumbaei-India) in nuclear physics at 2001.

He was working as professor of physics in department of physics Mazandaran University since, and currently occupied as head of nuclear physics department.

During last ten years, he published more than fifty papers in international journals, mostly in PRC, MPLB, IJMPE, and presented more than fifty papers in national and international conferences. He has guided more than 20 Ms.c student, 5 Ph.D student and taught several courses of Bs.c, Ms.c and Ph.D students of nuclear physics, mostly quantum mechanics, nuclear physics and classical mechanics for under graduate and graduate students.

Contents

**Preface IX** 

Anu Venugopalan

Chapter 2 **Time as Quantum Observable,** 

Chapter 3 **Order of Time Derivatives in** 

Chapter 4 **Theory of "Weak Value" and** 

Yutaka Shikano

Chapter 5 **Generalized Non-Relativistic** 

Chapter 6 **A Statistical Derivation of** 

Ulf Klein

Carsten Held

Chapter 8 **Quantum Correlations in** 

Ali Ahanj

D. White

Jan Jerzy Sławianowski

Chapter 1 **Measurement in Quantum Mechanics:** 

**Decoherence and the Pointer Basis 1** 

**Canonical Conjugated to Energy 17** 

**Quantum-Mechanical Equations 57** 

**Quantum Mechanical Measurements 75** 

**Supersymmetric Quantum Mechanics 101**  Thomas L. Markovich, Mason T. Biamonte,

**Non-Relativistic Quantum Theory 141** 

Eric R. Bittner and Donald J. Kouri

Chapter 7 **The Quantum Completeness Problem 175** 

**Successive Spin Measurements 197** 

Chapter 9 **The Gluon Emission Model for Vector Meson Decay 229** 

Vladislav S. Olkhovsky, Erasmo Recami and Sergei P. Maydanyuk

## Contents

#### **Preface XI**


D. White


## Preface

The volume Measurements in Quantum Mechanics explains different aspects of measurements in quantum mechanical systems. Understanding of quantum mechanics requires a careful definition of measurement. The subject of measurement is a basic part of the problem of the interpretation of quantum mechanics, for which there is currently no consensus. It is a postulate of quantum mechanics that all measurements have an associated observable. The quantum state of a system is a mathematical object that fully describes the quantum systems. From the inception of quantum mechanics, the concept of measurement proved to be a source of difficulties that found a concrete expression in the Einstein-Bohr debates, out of which both the Einstein Podolsky Rosen paradox and the Schrödinger's cat paradox developed. In brief, the difficulties stemmed from an apparent conflict between several principles of the quantum theory of measurement. In particular, the linear dynamics of quantum mechanics seemed to conflict with the postulate that during measurement a non-linear collapse of the wave packet occurred. The measurement problem is not just an interpretational difficulty internal to quantum mechanics. It raises broader issues as well, such as the philosophical debate between two different ideas. Quantum mechanics can be presented through concrete examples. I believe that most physicists learn through specific examples, test the obtained results through measurements and then find it easy to generalize. Spin measurements do not need sophisticated experimental devices, so the first postulate devoted through Estern-Gerlakh experiments of spin for measurements theory. Non-relativistic quantum mechanics has experienced a phase of turbulent development in the past few years. Quantum computing, quantum teleportation, quantum cryptography, and quantum information are typical buzzwords that reflect these developments. In spite of the enormous success of quantum mechanics to predict a wide range of physical phenomena, the quantum measurement problem through quantum mechanics is accepted as the fundamental theory of nature and gives satisfactory predictions to deduce the results of measurements.

This volume contains fourteen chapters that created by a group of invited authors from all over the world. A brief outline of the book is as follows:

Chapter one reviews the coherent and decoherent systems, which is the main goal of measurement theory. Time and energy as measurable quantities and their relations through uncertainty principal are discussed in chapter two. The different nature of time and energy as a parameter or observable in various parts of physics is also reviewed in this chapter. Chapter three deals with the order of time derivative in different branches of relativistic and nonrelativistic quantum mechanics. Dirac and Clain-Gordon equations, together with a group representation of subject, are also studied phenomenologically in this chapter. Chapter four covers the relation between the weak value theorem and the measurements in quantum mechanics. Supersymmetric quantum mechanics is presented in chapter five. Electronic structure of multielectron systems and their relation with the measurement is also discussed in this chapter. Chapter six relates to the statistical derivation of quantum mechanics, the probability to measure energy as a conjugate observable of time and the minimal Fisher information theory. Quantum completeness problem and its relation to quantum measurements are discussed in chapter seven. Chapter eight presented the quantum correlations in successive spin measurements. Application of multimeasurements results to spin <sup>1</sup> <sup>2</sup> systems and well-known Bell inequality are also discussed in this chapter. Spin coherent measurement, electron correlations in quantum chemistry and their application in gravitational bach ground are reported in chapter nine. Chapter ten deals with vector correlations in the collision of atom and diatomic molecule. Different types of mesons and their decay modes are also discussed in this chapter. Vector correlations in collision of atoms and diatomic molecules, their collision cross section and different angular distributions are reported in chapter eleven. Chapter twelve discusses the entanglement in two and three quantum mechanical systems and their relations with quantum mechanical measurements. Basic conventions of quantum chemistry and their relation with measurements in multi-electron systems, together with applications of this new model to maximize the intensity of images are reported in chapter thirteen. The last chapter deals with the Feynman loop integral in perturbative quantum field theory and their application in measurements of new type of colliders.

This book is a result of collaboration of the international community and I thank all the authors. I especially want to thank Ms. Maja Bozicevic for her valuable assistance through the publishing process and the InTech publishing team for their efforts in preparing the book for publication.

> **M. R. Pahlavani** Head of Nuclear Physics Department, Mazandaran University, Mazandaran, Babolsar, Iran
