SOME APPLICATIONS OF QUANTUM MECHANICS docx

SOME APPLICATIONS OF QUANTUM MECHANICS Edited by Mohammad Reza Pahlavani Some Applications of Quantum Mechanics Edited by Mohammad Reza Pahlavani Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2012 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. As for readers, this license allows users to download, copy and build upon published chapters even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Maja Bozicevic Technical Editor Teodora Smiljanic Cover Designer InTech Design Team First published February, 2012 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Some Applications of Quantum Mechanics, Edited by Mohammad Reza Pahlavani p. cm. ISBN 978-953-51-0059-1 Contents Preface IX Chapter 1 Quantum Phase-Space Transport and Applications to the Solid State Physics 1 Omar Morandi Chapter 2 Reaction Path Optimization and Sampling Methods and Their Applications for Rare Events 27 Peng Tao, Joseph D. Larkin and Bernard R. Brooks Chapter 3 Semiclassical Methods of Deformation Quantisation in Transport Theory 67 M. I. Krivoruchenko Chapter 4 Synergy Between First-Principles Computation and Experiment in Study of Earth Science 91 Shigeaki Ono Chapter 5 Quantum Mechanical Three-Body Systems and Its Application in Muon Catalyzed Fusion 109 S. M. Motevalli and M. R. Pahlavani Chapter 6 Application of Quantum Mechanics for Computing the Vibrational Spectra of Nitrogen Complexes in Silicon Nanomaterials 131 Faouzia Sahtout Karoui and Abdennaceur Karoui Chapter 7 Metal-Assisted Proton Transfer in Guanine-Cytosine Pair: An Approach from Quantum Chemistry 167 Toru Matsui, Hideaki Miyachi, Yasuteru Shigeta and Kimihiko Hirao Chapter 8 Quantum Mechanics on Surfaces 189 Bjørn Jensen VI Contents Chapter 9 Quantum Statistics and Coherent Access Hypothesis 215 Norton G. de Almeida Chapter 10 Flows of Information and Informational Trajectories in Chemical Processes 233 Nelson Flores-Gallegos and Carmen Salazar-Hernández Chapter 11 Quantum Mechanics Design of Two Photon Processes Based Solar Cells 257 Abdennaceur Karoui and Ara Kechiantz Chapter 12 Quantum Information-Theoretical Analyses of Systems and Processes of Chemical and Nanotechnological Interest 297 Rodolfo O. Esquivel, Edmundo M. Carrera, Cristina Iuga, Moyocoyani Molina-Espíritu, Juan Carlos Angulo, Jesús S. Dehesa, Sheila López-Rosa, Juan Antolín and Catalina Soriano-Correa Chapter 13 Quantum Computing and Optimal Control Theory 335 Kenji Mishima Chapter 14 Recent Applications of Hybrid Ab Initio Quantum Mechanics – Molecular Mechanics Simulations to Biological Macromolecules 359 Jiyoung Kang and Masaru Tateno Chapter 15 Battle of the Sexes: A Quantum Games Theory Approach 385 Juan Manuel López R. Chapter 16 Einstein-Bohr Controversy After 75 Years, Its Actual Solution and Consequences 409 Miloš V. Lokajiček Preface The volume Some Applications of Quantum Mechanics is intended to serve as a reference for Graduate level students as well as researchers from all fields of science. Quantum mechanics has been extremely successful in explaining microscopic phenomena in all branches of physics. Quantum mechanics is used on a daily basis by thousands of physicists, chemists and engineers. There were two revolutions in the way we viewed the physical world in the twentieth century: relativity and quantum mechanics. In quantum mechanics, the revolution was both profound, requiring a dramatic revision in the structure of the laws of mechanics that govern the behavior of all particles, be they electrons or photons, and determining the stability of matter itself, shaping the interactions of particles on the atomic, nuclear, and particle physics level, and leading to macroscopic quantum effects ranging from lasers and superconductivity to neutron stars and radiation from the black holes. We have always had a great deal of difficulty understanding the worldview that quantum mechanics represents. Quantum mechanics is often thought of as being the physics of the very small, as seen through its successes in describing the structure and properties of atoms and molecules (the chemical properties of matter), the structure of atomic nuclei and the properties of elementary particles. But this is true only insofar as the fact that peculiarly quantum elects are most readily observed at the atomic level. Beyond that, quantum mechanics is needed to explain radioactivity, how semiconducting devices (the backbone of modern high technology) work, and the origin of superconductivity, what makes a laser function. Although this book does not cover all areas of application of quantum mechanics, it is nevertheless a valuable effort by an international group of invited authors. I believed that it is necessary to publish at least one volume for each type of the enormous applications of quantum mechanics. This book is contains sixteen chapters and its brief outline is as follows: Chapters one to five provide some methods to solve the Schrodinger equation in different areas of science. Chapter six describes the application of quantum mechanics in three-body systems, which are mostly used in fusion phenomena as an attractive part of nuclear physics. Applications of quantum mechanics in solid-state physics and nanotechnology are described well in chapter seven. Chapter eight covers the applications of quantum mechanics in biotechnology, for analyzing Ciplatin bounds in DNA. A study of a different surface in non-relativistic and relativistic reference frame using quantum mechanics is presented in chapter nine. Quantum Hall effect, X Preface superconductivity and related subjects using fractional statistic in quantum mechanics are covered in chapter ten. Chemical processes and quantum chemistry are discussed in chapter eleven. The application of quantum mechanics in photo electronic properties of semiconductors to study the effect of two-photon absorption in solar cells is discussed in chapter twelve. Chapter thirteen is related to quantum mechanical study of multi electronic systems and their relation to information theory and thermodynamical properties of Microsystems. Quantum computing and quantum information science are presented as a fresh and attractive research area of applied science in chapter fourteen. Chapter fifteen describes the hybrid ab initio quantum mechanics applied to investigate the molecular structure of biological macromolecules. The final chapter, chapter sixteen, deals with the application of game theory to predict the battle of sex using matrix representation of quantum mechanics, accompanied with related statistics. This collection is written by an international group of invited scientists and researchers and I gratefully acknowledge their collaboration in this project. I would like to thank Ms. Maja Bozicevic for her valuable assistance in different stages of the project, and the InTech publishing team for creating this opportunity for scientists and researchers to communicate and publish this book. Mohammad Reza Pahlavani Head of Nuclear Physics Department, Mazandaran University, Mazandaran, Babolsar, Iran [...]... representations The applications of this formalism span among different subjects: the 2 2 Some Applications of Quantum Mechanics Will-be-set-by-IN-TECH multi-band transport and its applications to nano-devices, quasi classical approximations of the motion and the characterization of a system in terms of Berry phases or, more generally, the representation of a quantum system by means of a Riemann manifold with... for the full quantum description of the electron transport with the inclusion of the interband processes Among them, the phase-space formulation of quantum mechanics offers a framework in which the quantum phenomena can be described with a classical language and the question of the quantum- classical correspondence can be directly investigated In particular, the visual representation of the quantum mechanical... ∂r A ∂p 8 Some Applications of Quantum Mechanics Will-be-set-by-IN-TECH 8 3.1 Generalization of the Wigner-Moyal map A separable Hilbert space can be characterized by a complete set of basis elements ψi or, equivalently, by a unitary transformation Θ (defined in terms of the projection of the ψi set on a reference basis) The class of unitary operators C(Θ ) defines all the alternative sets of basis elements... adiabatic theory ensures that the second term on the right side of the equation becomes arbitrarily small in the limit of sufficiently slow-in-time evolution of the momentum p (quasi-static or adiabatic hypothesis) An introduction to the adiabatic theory containing a 18 Some Applications of Quantum Mechanics Will-be-set-by-IN-TECH 18 rigorous proof of this statement presented in a general context, can be found... class of equivalent quasi-distribution functions The applications of this formalism span among different subjects: the multi-band transport in nano-devices, the infinite-order h-approximations of the motion and the characterization of a system in terms of Berry phases ¯ or, more generally, the representation of a quantum system by means of a Riemann manifold with a suitable connection The exposition of. .. 12 Some Applications of Quantum Mechanics Will-be-set-by-IN-TECH 3.3 Application to multiband structures: correction to the classical trajectory in semiconductors We investigate the application of the multiband Wigner formalism to the semiconductor structures The study of the particle motion in semiconductors has attracted the scientific community, e g., to the sometime anti-intuitive properties of. .. oscillations (whose frequency is of the order of Eg /¯ ) which, h up to zero order in h, decouple hcv from the slowly varying functions hc and hv This aspect ¯ is examined in sec 3.4 We explore the single band limit of Eqs (38)-(40) From the physical point of view, we expect that when the electric field goes to zero or the band gap goes to 14 Some Applications of Quantum Mechanics Will-be-set-by-IN-TECH... following definition of Fourier transform 4 Some Applications of Quantum Mechanics Will-be-set-by-IN-TECH 4 f = F p → η [ f ]: f = f = f (r, p )e−ip ·η dp Rd p 1 (2π )d f (η, p )eip ·η dη Rd η The remarkable difference between the quantum phase-space equation of motion and the classical analogous (Liouville equation) ∂f p = − · ∇r f − E (r) · ∇p f , ∂t m (6) is constituted by the presence of the pseudo-differential... suitable connection We discuss some results obtained in this contexts by presenting the major lines of the derivation of the models and their applications Particular emphasis is devoted to present the methods used for the approximation of the solution The latter is a particularly important aspect of the theory, but often underestimated: the description of a system in the quantum phase-space usually involves... Taylor expansion, all of the p operators appearing in the expansion of A (r, p) follow (precede) the r operators A different choice is made in the Weyl ordering rule where each polynomial of the p and r variables is mapped, term by term, in a completely 6 Some Applications of Quantum Mechanics Will-be-set-by-IN-TECH 6 ordered expression of r and p The generic binomial p m rn becomes (see i e (Zachos et . SOME APPLICATIONS OF QUANTUM MECHANICS Edited by Mohammad Reza Pahlavani Some Applications of Quantum Mechanics Edited by Mohammad Reza. relativity and quantum mechanics. In quantum mechanics, the revolution was both profound, requiring a dramatic revision in the structure of the laws of mechanics that govern the behavior of all particles,. part of nuclear physics. Applications of quantum mechanics in solid-state physics and nanotechnology are described well in chapter seven. Chapter eight covers the applications of quantum mechanics