Mathematical Methods Of Classical Mechanics

Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 1475720637
Size: 39.12 MB
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This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Advanced Quantum Mechanics

Author: Rainer Dick
Publisher: Springer
ISBN: 3319256750
Size: 47.44 MB
Format: PDF
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In this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics, Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of quantum electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquired an understanding of basic quantum mechanics and classical field theory, canonical field quantization is easy. Furthermore, the integrated discussion of transition a mplitudes naturally leads to the notions of transition probabilities, decay rates, absorption cross sections and scattering cross sections, which are important for all experimental techniques that use photon probes. Quantization is first discussed for the Schrödinger field before the relativistic Maxwell, Klein-Gordon and Dirac fields are quantized. Quantized Schrödinger field theory is not only important for condensed matter physics and materials science, but also provides the easiest avenue to general field quantization and is therefore also useful for students with an interest in nuclear and particle physics. The quantization of the Maxwell field is performed in Coulomb gauge. This is the appropriate and practically most useful quantization procedure in condensed matter physics, chemistry, and materials science because it naturally separates the effects of Coulomb interactions, exchange interactions, and photon scattering. The appendices contain additional material that is usually not found in standard quantum mechanics textbooks, including a completeness proof for eigenfunctions of one-dimensional Sturm-Liouville problems, logarithms of matrices, and Green’s functions in different dimensions.

Fluid Dynamics

Author: Michel Rieutord
Publisher: Springer
ISBN: 3319093517
Size: 74.77 MB
Format: PDF
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This book is dedicated to readers who want to learn fluid dynamics from the beginning. It assumes a basic level of mathematics knowledge that would correspond to that of most second-year undergraduate physics students and examines fluid dynamics from a physicist’s perspective. As such, the examples used primarily come from our environment on Earth and, where possible, from astrophysics. The text is arranged in a progressive and educational format, aimed at leading readers from the simplest basics to more complex matters like turbulence and magnetohydrodynamics. Exercises at the end of each chapter help readers to test their understanding of the subject (solutions are provided at the end of the book), and a special chapter is devoted to introducing selected aspects of mathematics that beginners may not be familiar with, so as to make the book self-contained.

Theoretical Mechanics

Author: Reiner M. Dreizler
Publisher: Springer Science & Business Media
ISBN: 9783642111389
Size: 71.30 MB
Format: PDF, Mobi
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This book is the first of a series covering the major topics that are taught in university courses in Theoretical Physics: Mechanics, Electrodynamics, Quantum Theory and Statistical Physics. After an introduction to basic concepts of mechanics more advanced topics build the major part of this book. Interspersed is a discussion of selected problems of motion. This is followed by a concise treatment of the Lagrangian and the Hamiltonian formulation of mechanics, as well as a brief excursion on chaotic motion. The last chapter deals with applications of the Lagrangian formulation to specific systems (coupled oscillators, rotating coordinate systems, rigid bodies). The level of the last sections is advanced. The text is accompanied by an extensive collection of online material, in which the possibilities of the electronic medium are fully exploited, e.g. in the form of applets, 2D- and 3D-animations. It contains: A collection of 74 problems with detailed step-by-step guidance towards the solutions, a collection of comments and additional mathematical details in support of the main text, a complete presentation of all the mathematical tools needed.

Elementary Lectures In Statistical Mechanics

Author: George D.J. Phillies
Publisher: Springer Science & Business Media
ISBN: 9780387989181
Size: 75.60 MB
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This book presents the major areas of statistical mechanics and concludes with a demonstration of applications of statistical mechanics at the level of current research. The presentation begins with the fundamental ideas of averages and ensembles, focusing on classical systems described by continuous variables such as position and momentum. It then turns to quantum systems, beginning with diatomic molecules and working up through blackbody radiation and chemical equilibria.

The Variational Principles Of Mechanics

Author: Cornelius Lanczos
Publisher: Courier Corporation
ISBN: 0486134709
Size: 51.15 MB
Format: PDF, ePub, Mobi
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Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.

Quantum Theory For Mathematicians

Author: Brian C. Hall
Publisher: Springer Science & Business Media
ISBN: 1461471168
Size: 35.36 MB
Format: PDF, Mobi
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Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

Statistical Mechanics Theory And Molecular Simulation

Author: Mark Tuckerman
Publisher: OUP Oxford
ISBN: 9780191523465
Size: 37.33 MB
Format: PDF, Mobi
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Complex systems that bridge the traditional disciplines of physics, chemistry, biology, and materials science can be studied at an unprecedented level of detail using increasingly sophisticated theoretical methodology and high-speed computers. The aim of this book is to prepare burgeoning users and developers to become active participants in this exciting and rapidly advancing research area by uniting for the first time, in one monograph, the basic concepts of equilibrium and time-dependent statistical mechanics with the modern techniques used to solve the complex problems that arise in real-world applications. The book contains a detailed review of classical and quantum mechanics, in-depth discussions of the most commonly used ensembles simultaneously with modern computational techniques such as molecular dynamics and Monte Carlo, and important topics including free-energy calculations, linear-response theory, harmonic baths and the generalized Langevin equation, critical phenomena, and advanced conformational sampling methods. Burgeoning users and developers are thus provided firm grounding to become active participants in this exciting and rapidly advancing research area, while experienced practitioners will find the book to be a useful reference tool for the field.


Author: Florian A. Scheck
Publisher: Springer Science & Business Media
ISBN: 3662029731
Size: 43.82 MB
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Purpose and Emphasis. Mechanics not only is the oldest branch of physics but was and still is the basis for all of theoretical physics. Quantum mechanics can hardly be understood, perhaps cannot even be formulated, without a good knowledge of general mechanics. Field theories such as electrodynamics borrow their formal framework and many of their building principles from mechanics. In short, throughout the many modem developments of physics where one fre quently turns back to the principles of c1assical mechanics its model character is feIt. For this reason it is not surprising that the presentation of mechanics reflects to some extent the development of modem physics and that today this c1assical branch of theoretical physics is taught rather differently than at the time of Arnold Sommerfeld, in the 1920s, or even in the 1950s, when more emphasis was put on the theory and the applications of partial-differential equations. Today, symme tries and invariance principles, the structure ofthespace-time continuum, and the geometrical structure of mechanics play an important role. The beginner should realize that mechanics is not primarily the art of describing block-and-tackles, coIIisions of billiard balls, constrained motions of the cylinder in a washing ma chine, or bicycle riding.