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Solving The Schrdinger Equation
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Book Synopsis Solving the Schrodinger Equation by : Paul L. A. Popelier
Download or read book Solving the Schrodinger Equation written by Paul L. A. Popelier and published by World Scientific. This book was released on 2011 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Schrodinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrodinger equation. Each method is based on a set of core ideas and this volume aims to explain these ideas clearly so that they become more accessible. By bringing together these non-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of novel approaches. Is there a method out there that we have not thought of yet? Can we design a new method that combines the best of all worlds?
Book Synopsis A Student's Guide to the Schrödinger Equation by : Daniel A. Fleisch
Download or read book A Student's Guide to the Schrödinger Equation written by Daniel A. Fleisch and published by Cambridge University Press. This book was released on 2020-02-20 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear guide to the key concepts and mathematical techniques underlying the Schrödinger equation, including homework problems and fully worked solutions.
Book Synopsis Physical Chemistry for the Biosciences by : Raymond Chang
Download or read book Physical Chemistry for the Biosciences written by Raymond Chang and published by University Science Books. This book was released on 2005-02-11 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is ideal for use in a one-semester introductory course in physical chemistry for students of life sciences. The author's aim is to emphasize the understanding of physical concepts rather than focus on precise mathematical development or on actual experimental details. Subsequently, only basic skills of differential and integral calculus are required for understanding the equations. The end-of-chapter problems have both physiochemical and biological applications.
Book Synopsis Handbook of Exact Solutions to the Nonlinear Schrödinger Equations (Second Edition) by : USAMA. AL KHAWAJA
Download or read book Handbook of Exact Solutions to the Nonlinear Schrödinger Equations (Second Edition) written by USAMA. AL KHAWAJA and published by Institute of Physics Publishing. This book was released on 2024-06-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optical Communication Theory and Techniques by : Enrico Forestieri
Download or read book Optical Communication Theory and Techniques written by Enrico Forestieri and published by Springer Science & Business Media. This book was released on 2006-01-26 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the advent of optical communications, a greattechnological effort has been devoted to the exploitation of the huge bandwidth of optical fibers. Sta- ing from a few Mb/s single channel systems, a fast and constant technological development has led to the actual 10 Gb/s per channel dense wavelength - vision multiplexing (DWDM) systems, with dozens of channels on a single fiber. Transmitters and receivers are now ready for 40 Gb/s, whereas hundreds of channels can be simultaneously amplified by optical amplifiers. Nevertheless, despite such a pace in technological progress, optical c- munications are still in a primitive stage if compared, for instance, to radio communications: the widely spread on-off keying (OOK) modulation format is equivalent to the rough amplitude modulation (AM) format, whereas the DWDM technique is nothing more than the optical version of the frequency - vision multiplexing (FDM) technique. Moreover, adaptive equalization, ch- nel coding or maximum likelihood detection are still considered something “exotic” in the optical world. This is mainly due to the favourable char- teristics of the fiber optic channel (large bandwidth, low attenuation, channel stability, ...), which so far allowed us to use very simple transmission and detection techniques.
Book Synopsis The Schrödinger Equation by : F.A. Berezin
Download or read book The Schrödinger Equation written by F.A. Berezin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with those topics of mathematical physics, associated with the study of the Schrödinger equation, which are considered to be the most important. Chapter 1 presents the basic concepts of quantum mechanics. Chapter 2 provides an introduction to the spectral theory of the one-dimensional Schrödinger equation. Chapter 3 opens with a discussion of the spectral theory of the multi-dimensional Schrödinger equation, which is a far more complex case and requires careful consideration of aspects which are trivial in the one-dimensional case. Chapter 4 presents the scattering theory for the multi-dimensional non-relativistic Schrödinger equation, and the final chapter is devoted to quantization and Feynman path integrals. These five main chapters are followed by three supplements, which present material drawn on in the various chapters. The first two supplements deal with general questions concerning the spectral theory of operators in Hilbert space, and necessary information relating to Sobolev spaces and elliptic equations. Supplement 3, which essentially stands alone, introduces the concept of the supermanifold which leads to a more natural treatment of quantization. Although written primarily for mathematicians who wish to gain a better awareness of the physical aspects of quantum mechanics and related topics, it will also be useful for mathematical physicists who wish to become better acquainted with the mathematical formalism of quantum mechanics. Much of the material included here has been based on lectures given by the authors at Moscow State University, and this volume can also be recommended as a supplementary graduate level introduction to the spectral theory of differential operators with both discrete and continuous spectra. This English edition is a revised, expanded version of the original Soviet publication.
Book Synopsis Introduction to Optical Waveguide Analysis by : Kenji Kawano
Download or read book Introduction to Optical Waveguide Analysis written by Kenji Kawano and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete survey of modern design and analysis techniques for optical waveguides This volume thoroughly details modern and widely accepted methods for designing the optical waveguides used in telecommunications systems. It offers a straightforward presentation of the sophisticated techniques used in waveguide analysis and enables a quick grasp of modern numerical methods with easy mathematics. The book is intended to guide the reader to a comprehensive understanding of optical waveguide analysis through self-study. This comprehensive presentation includes: * An extensive and exhaustive list of mathematical manipulations * Detailed explanations of common design methods: finite element method (FEM), finite difference method (FDM), beam propagation method (BPM), and finite difference time-domain method (FD-TDM) * Explanations for numerical solutions of optical waveguide problems with sophisticated techniques used in modern computer-aided design (CAD) software * Solutions to Maxwell's equations and the Schrodinger equation The authors provide excellent self-study material for practitioners, researchers, and students, while also presenting detailed mathematical manipulations that can be easily understood by readers who are unfamiliar with them. Introduction to Optical Waveguide Analysis presents modern design methods in a comprehensive and easy-to-understand format.
Book Synopsis Collected Papers on Wave Mechanics by : Erwin Schrödinger
Download or read book Collected Papers on Wave Mechanics written by Erwin Schrödinger and published by American Mathematical Soc.. This book was released on 2003 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The famous equation that bears Erwin Schrödinger's name encapsulates his profound contributions to quantum mechanics using wave mechanics. This third, augmented edition of his papers on the topic contains the six original, famous papers in which Schrödinger created and developed the subject of wave mechanics as published in the original edition. As the author points out, at the time each paper was written the results of the later papers were largely unknown to him. This edition also contains three papers that were written shortly after the original edition was published and four lectures delivered by Schrödinger at the Royal Institution in London in 1928. The papers and lectures in this volume were revised by the author and translated into English, and afford the reader a striking and valuable insight into how wave mechanics developed.
Download or read book University Physics written by OpenStax and published by . This book was released on 2016-11-04 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result. The text and images in this textbook are grayscale.
Book Synopsis Quantum Physics For Dummies by : Steven Holzner
Download or read book Quantum Physics For Dummies written by Steven Holzner and published by John Wiley & Sons. This book was released on 2013-01-09 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Your plain-English guide to understanding and working with the micro world Quantum Physics For Dummies, Revised Edition helps make quantum physics understandable and accessible. From what quantum physics can do for the world to understanding hydrogen atoms, readers will get complete coverage of the subject, along with numerous examples to help them tackle the tough equations. Compatible with classroom text books and courses, Quantum Physics For Dummies, Revised Edition lets students study at their own paces and helps them prepare for graduate or professional exams. Coverage includes: The Schrodinger Equation and its Applications The Foundations of Quantum Physics Vector Notation Spin Scattering Theory, Angular Momentum, and more Quantum physics — also called quantum mechanics or quantum field theory — can be daunting for even the most dedicated student or enthusiast of science, math, or physics. This friendly, concise guide makes this challenging subject understandable and accessible, from atoms to particles to gases and beyond. Plus, it's packed with fully explained examples to help you tackle the tricky equations like a pro! Compatible with any classroom course — study at your own pace and prepare for graduate or professional exams Your journey begins here — understand what quantum physics is and what kinds of problems it can solve Know the basic math — from state vectors to quantum matrix manipulations, get the foundation you need to proceed Put quantum physics to work — make sense of Schrödinger's equation and handle particles bound in square wells and harmonic oscillators Solve problems in three dimensions — use the full operators to handle wave functions and eigenvectors to find the natural wave functions of a system Discover the latest research — learn the cutting-edge quantum physics theories that aim to explain the universe itself
Book Synopsis Direct and Inverse Scattering for the Matrix Schrödinger Equation by : Tuncay Aktosun
Download or read book Direct and Inverse Scattering for the Matrix Schrödinger Equation written by Tuncay Aktosun and published by Springer Nature. This book was released on 2020-05-19 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.
Book Synopsis Conceptual Foundations Of Quantum Mechanics by : Bernard D'espagnat
Download or read book Conceptual Foundations Of Quantum Mechanics written by Bernard D'espagnat and published by CRC Press. This book was released on 2018-03-05 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conceptual Foundations of Quantum Mechanics provides a detailed view of the conceptual foundations and problems of quantum physics, and a clear and comprehensive account of the fundamental physical implications of the quantum formalism. This book deals with nonseparability, hidden variable theories, measurement theories and several related problems. Mathematical arguments are presented with an emphasis on simple but adequately representative cases. The conclusion incorporates a description of a set of relationships and concepts that could compose a legitimate view of the world.
Book Synopsis A Textbook of Physical Chemistry – Volume 1 by : Mandeep Dalal
Download or read book A Textbook of Physical Chemistry – Volume 1 written by Mandeep Dalal and published by Dalal Institute. This book was released on 2018-01-01 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced-level textbook of physical chemistry for the graduate (B.Sc) and postgraduate (M.Sc) students of Indian and foreign universities. This book is a part of four volume series, entitled "A Textbook of Physical Chemistry – Volume I, II, III, IV". CONTENTS: Chapter 1. Quantum Mechanics – I: Postulates of quantum mechanics; Derivation of Schrodinger wave equation; Max-Born interpretation of wave functions; The Heisenberg’s uncertainty principle; Quantum mechanical operators and their commutation relations; Hermitian operators (elementary ideas, quantum mechanical operator for linear momentum, angular momentum and energy as Hermition operator); The average value of the square of Hermitian operators; Commuting operators and uncertainty principle(x & p; E & t); Schrodinger wave equation for a particle in one dimensional box; Evaluation of average position, average momentum and determination of uncertainty in position and momentum and hence Heisenberg’s uncertainty principle; Pictorial representation of the wave equation of a particle in one dimensional box and its influence on the kinetic energy of the particle in each successive quantum level; Lowest energy of the particle. Chapter 2. Thermodynamics – I: Brief resume of first and second Law of thermodynamics; Entropy changes in reversible and irreversible processes; Variation of entropy with temperature, pressure and volume; Entropy concept as a measure of unavailable energy and criteria for the spontaneity of reaction; Free energy, enthalpy functions and their significance, criteria for spontaneity of a process; Partial molar quantities (free energy, volume, heat concept); Gibb’s-Duhem equation. Chapter 3. Chemical Dynamics – I: Effect of temperature on reaction rates; Rate law for opposing reactions of Ist order and IInd order; Rate law for consecutive & parallel reactions of Ist order reactions; Collision theory of reaction rates and its limitations; Steric factor; Activated complex theory; Ionic reactions: single and double sphere models; Influence of solvent and ionic strength; The comparison of collision and activated complex theory. Chapter 4. Electrochemistry – I: Ion-Ion Interactions: The Debye-Huckel theory of ion- ion interactions; Potential and excess charge density as a function of distance from the central ion; Debye Huckel reciprocal length; Ionic cloud and its contribution to the total potential; Debye - Huckel limiting law of activity coefficients and its limitations; Ion-size effect on potential; Ion-size parameter and the theoretical mean-activity coefficient in the case of ionic clouds with finite-sized ions; Debye - Huckel-Onsager treatment for aqueous solutions and its limitations; Debye-Huckel-Onsager theory for non-aqueous solutions; The solvent effect on the mobality at infinite dilution; Equivalent conductivity (Λ) vs. concentration c 1/2 as a function of the solvent; Effect of ion association upon conductivity (Debye- Huckel - Bjerrum equation). Chapter 5. Quantum Mechanics – II: Schrodinger wave equation for a particle in a three dimensional box; The concept of degeneracy among energy levels for a particle in three dimensional box; Schrodinger wave equation for a linear harmonic oscillator & its solution by polynomial method; Zero point energy of a particle possessing harmonic motion and its consequence; Schrodinger wave equation for three dimensional Rigid rotator; Energy of rigid rotator; Space quantization; Schrodinger wave equation for hydrogen atom, separation of variable in polar spherical coordinates and its solution; Principle, azimuthal and magnetic quantum numbers and the magnitude of their values; Probability distribution function; Radial distribution function; Shape of atomic orbitals (s,p & d). Chapter 6. Thermodynamics – II: Classius-Clayperon equation; Law of mass action and its thermodynamic derivation; Third law of thermodynamics (Nernest heat theorem, determination of absolute entropy, unattainability of absolute zero) and its limitation; Phase diagram for two completely miscible components systems; Eutectic systems, Calculation of eutectic point; Systems forming solid compounds Ax By with congruent and incongruent melting points; Phase diagram and thermodynamic treatment of solid solutions. Chapter 7. Chemical Dynamics – II: Chain reactions: hydrogen-bromine reaction, pyrolysis of acetaldehyde, decomposition of ethane; Photochemical reactions (hydrogen - bromine & hydrogen -chlorine reactions); General treatment of chain reactions (ortho-para hydrogen conversion and hydrogen - bromine reactions); Apparent activation energy of chain reactions, Chain length; Rice-Herzfeld mechanism of organic molecules decomposition(acetaldehyde); Branching chain reactions and explosions ( H2-O2 reaction); Kinetics of (one intermediate) enzymatic reaction : Michaelis-Menton treatment; Evaluation of Michaelis 's constant for enzyme-substrate binding by Lineweaver-Burk plot and Eadie-Hofstae methods; Competitive and non-competitive inhibition. Chapter 8. Electrochemistry – II: Ion Transport in Solutions: Ionic movement under the influence of an electric field; Mobility of ions; Ionic drift velocity and its relation with current density; Einstein relation between the absolute mobility and diffusion coefficient; The Stokes- Einstein relation; The Nernst -Einstein equation; Walden’s rule; The Rate-process approach to ionic migration; The Rate process equation for equivalent conductivity; Total driving force for ionic transport, Nernst - Planck Flux equation; Ionic drift and diffusion potential; the Onsager phenomenological equations; The basic equation for the diffusion; Planck-Henderson equation for the diffusion potential.
Book Synopsis Nonlinear Fiber Optics by : Govind P. Agrawal
Download or read book Nonlinear Fiber Optics written by Govind P. Agrawal and published by Academic Press. This book was released on 2007 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the 3rd edition appeared, a fast evolution of the field has occurred. The fourth edition of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers. The contents include such important topics as self- and cross-phase modulation, stimulated Raman and Brillouin scattering, four-wave mixing, modulation instability, and optical solitons. Many new figures have been added to help illustrate the concepts discussed in the book. New to this edition are chapters on highly nonlinear fibers and and the novel nonlinear effects that have been observed in these fibers since 2000. Such a chapter should be of interest to people in the field of new wavelengths generation, which has potential application in medical diagnosis and treatments, spectroscopy, new wavelength lasers and light sources, etc. Continues to be industry bestseller providing unique source of comprehensive coverage on the subject of nonlinear fiber optics Fourth Edition is a completely up-to-date treatment of the nonlinear phenomena occurring inside optical fibers Includes 2 NEW CHAPTERS on the properties of highly nonlinear fibers and their novel nonlinear effects
Book Synopsis Group Theory in Solid State Physics and Photonics by : Wolfram Hergert
Download or read book Group Theory in Solid State Physics and Photonics written by Wolfram Hergert and published by John Wiley & Sons. This book was released on 2018-08-20 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals. Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic applications are discussed in parallel to the electronic case, with the focus on photonic crystals in two and three dimensions, as well as being partially expanded to other problems in the field of photonics. The authors have developed Mathematica package GTPack which is available for download from the book's homepage. Analytic considerations, numerical calculations and visualization are carried out using the same software. While the use of the Mathematica tools are demonstrated on elementary examples, they can equally be applied to more complicated tasks resulting from the reader's own research.
Book Synopsis The Meaning of the Wave Function by : Shan Gao
Download or read book The Meaning of the Wave Function written by Shan Gao and published by Cambridge University Press. This book was released on 2017-03-16 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering much of the recent debate, this ambitious text provides new, decisive proof of the reality of the wave function.
Book Synopsis Many-Body Methods in Chemistry and Physics by : Isaiah Shavitt
Download or read book Many-Body Methods in Chemistry and Physics written by Isaiah Shavitt and published by Cambridge University Press. This book was released on 2009-08-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the mathematical and diagrammatic techniques employed in the popular many-body methods to determine molecular structure, properties and interactions.
