INTRODUCTION TO QUANTUM MECHANICSSCHRODINGER EQUATION AND PATH INTEGRAL

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Author : Harald J W MÃ¼ller-Kirsten
ISBN : 9789814397766
Genre : Science
File Size : 41.30 MB
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This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrödinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions. In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.

Author : H. J. W. Mller-Kirsten
ISBN : 9789812566911
Genre : Science
File Size : 39.39 MB
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After a consideration of basic quantum mechanics, this introduction aims at a side by side treatment of fundamental applications of the Schrdinger equation on the one hand and the applications of the path integral on the other. Different from traditional texts and using a systematic perturbation method, the solution of Schrdinger equations includes also those with anharmonic oscillator potentials, periodic potentials, screened Coulomb potentials and a typical singular potential, as well as the investigation of the large order behavior of the perturbation series. On the path integral side, after introduction of the basic ideas, the expansion around classical configurations in Euclidean time, such as instantons, is considered, and the method is applied in particular to anharmonic oscillator and periodic potentials. Numerous other aspects are treated on the way, thus providing the reader an instructive overview over diverse quantum mechanical phenomena, e.g. many other potentials, Green's functions, comparison with WKB, calculation of lifetimes and sojourn times, derivation of generating functions, the Coulomb problem in various coordinates, etc. All calculations are given in detail, so that the reader can follow every step.

Author : Paul Popelier
ISBN : 9781908977762
Genre : Science
File Size : 49.24 MB
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The Schrödinger 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 Schrödinger 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? Contents:Intracule Functional Theory (Deborah L Crittenden and Peter M W Gill)Explicitly Correlated Electronic Structure Theory (Frederick R Manby)Solving Problems with Strong Correlation Using the Density Matrix Renormalization Group (DMRG) (Garnet Kin-Lic Chan and Sandeep Sharma)Reduced-Density-Matrix Theory for Many-electron Correlation (David A Mazziotti)Finite Size Scaling for Criticality of the Schrödinger Equation (Sabre Kais)The Generalized Sturmian Method (James Avery and John Avery)Slater-Type Orbital Basis Sets: Reliable and Rapid Solution of the Schrödinger Equation for Accurate Molecular Properties (Philip E Hoggan)Modern Ab Initio Valence Bond Methods (Philippe C Hiberty & Sason Shaik)Quantum Monte Carlo Approaches for Tackling Electronic Correlation (Massimo Mella and Gabriele Morosi)Solving the Schrödinger Equation on Real-Space Grids and with Random Walks (Thomas L Beck and Joel H Dedrick)Changes in Dense Linear Algebra Kernels: Decades-Long Perspective (Piotr Luszczek, Jakub Kurzak, and Jack Dongarra) Readership: Graduate students, postdoctoral researchers and academics in the fields of computational chemistry, theoretical chemistry, super computing, molecular physics and solid state physics. Keywords:Quantum Mechanics;Quantum Chemistry;Molecular Electronic SchrÃ¶dinger EquationKey Features:Unusual combination of methods/techniquesA thought-provoking and didactic exposé, not a review, nor a textbookLooks at the future

Author : Harald J W MÃ¼ller-Kirsten
ISBN : 9789814449557
Genre : Science
File Size : 52.68 MB
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Statistics links microscopic and macroscopic phenomena, and requires for this reason a large number of microscopic elements like atoms. The results are values of maximum probability or of averaging. This introduction to statistical physics concentrates on the basic principles, and attempts to explain these in simple terms supplemented by numerous examples. These basic principles include the difference between classical and quantum statistics, a priori probabilities as related to degeneracies, the vital aspect of indistinguishability as compared with distinguishability in classical physics, the differences between conserved and non-conserved elements, the different ways of counting arrangements in the three statistics (Maxwell–Boltzmann, Fermi–Dirac, Bose–Einstein), the difference between maximization of the number of arrangements of elements, and averaging in the Darwin–Fowler method. Significant applications to solids, radiation and electrons in metals are treated in separate chapters, as well as Bose–Einstein condensation. This revised second edition contains an additional chapter on the Boltzmann transport equation along with appropriate applications. Also, more examples have been added throughout, as well as further references to literature.

Author : Jean Zinn-Justin
ISBN : 9780198566755
Genre : Mathematics
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Quantum field theory is hardly comprehensible without path integrals: the goal of this book is to introduce students to this topic within the context of ordinary quantum mechanics and non-relativistic many-body theory, before facing the problems associated with the more involved quantum field theory formalism.

Ideas of Quantum Chemistry shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. Ideas of Quantum Chemistry has both textbook and reference work aspects. Like a textbook, the material is organized into digestable sections with each chapter following the same structure. It answers frequently asked questions and highlights the most important conclusions and the essential mathematical formulae in the text. In its reference aspects, it has a broader range than traditional quantum chemistry books and reviews virtually all of the pertinent literature. It is useful both for beginners as well as specialists in advanced topics of quantum chemistry. The book is supplemented by an appendix on the Internet. * Presents the widest range of quantum chemical problems covered in one book * Unique structure allows material to be tailored to the specific needs of the reader * Informal language facilitates the understanding of difficult topics

Author : David A. B. Miller
ISBN : 9781139471275
Genre : Technology & Engineering
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If you need a book that relates the core principles of quantum mechanics to modern applications in engineering, physics, and nanotechnology, this is it. Students will appreciate the book's applied emphasis, which illustrates theoretical concepts with examples of nanostructured materials, optics, and semiconductor devices. The many worked examples and more than 160 homework problems help students to problem solve and to practise applications of theory. Without assuming a prior knowledge of high-level physics or classical mechanics, the text introduces Schrödinger's equation, operators, and approximation methods. Systems, including the hydrogen atom and crystalline materials, are analyzed in detail. More advanced subjects, such as density matrices, quantum optics, and quantum information, are also covered. Practical applications and algorithms for the computational analysis of simple structures make this an ideal introduction to quantum mechanics for students of engineering, physics, nanotechnology, and other disciplines. Additional resources available from www.cambridge.org/9780521897839.