The Weierstrass Elliptic Function And Applications In Classical And Quantum Mechanics

Author : Georgios Pastras
Publisher : Springer Nature
Page : 111 pages
File Size : 47,6 Mb
Release : 2020-10-31
Category : Science
ISBN : 9783030593858

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The Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics by Georgios Pastras Pdf

The field of elliptic functions, apart from its own mathematical beauty, has many applications in physics in a variety of topics, such as string theory or integrable systems. This book, which focuses on the Weierstrass theory of elliptic functions, aims at senior undergraduate and junior graduate students in physics or applied mathematics. Supplemented by problems and solutions, it provides a fast, but thorough introduction to the mathematical theory and presents some important applications in classical and quantum mechanics. Elementary applications, such as the simple pendulum, help the readers develop physical intuition on the behavior of the Weierstrass elliptic and related functions, whereas more Interesting and advanced examples, like the n=1 Lamé problem-a periodic potential with an exactly solvable band structure, are also presented.

Author : William A. Schwalm
Publisher : Morgan & Claypool Publishers
Page : 57 pages
File Size : 50,9 Mb
Release : 2015-12-31
Category : Science
ISBN : 9781681740386

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Lectures on Selected Topics in Mathematical Physics by William A. Schwalm Pdf

This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first and second year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.

Author : Alain J Brizard
Publisher : World Scientific Publishing Company
Page : 324 pages
File Size : 52,8 Mb
Release : 2014-11-28
Category : Science
ISBN : 9789814623643

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An Introduction to Lagrangian Mechanics by Alain J Brizard Pdf

An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler–Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory. The Second Edition includes a larger selection of examples and problems (with hints) in each chapter and continues the strong emphasis of the First Edition on the development and application of mathematical methods (mostly calculus) to the solution of problems in Classical Mechanics. New material has been added to most chapters. For example, a new derivation of the Noether theorem for discrete Lagrangian systems is given and a modified Rutherford scattering problem is solved exactly to show that the total scattering cross section associated with a confined potential (i.e., which vanishes beyond a certain radius) yields the hard-sphere result. The Frenet-Serret formulas for the Coriolis-corrected projectile motion are presented, where the Frenet-Serret torsion is shown to be directly related to the Coriolis deflection, and a new treatment of the sleeping-top problem is given.

Author : Alain Jean Brizard
Publisher : World Scientific
Page : 276 pages
File Size : 45,9 Mb
Release : 2008
Category : Science
ISBN : 9789812818362

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An Introduction to Lagrangian Mechanics by Alain Jean Brizard Pdf

An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler?Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory.This textbook is suitable for undergraduate students who have acquired the mathematical skills needed to complete a course in Modern Physics.

Author : Frank W. J. Olver
Publisher : Cambridge University Press
Page : 968 pages
File Size : 42,7 Mb
Release : 2010-05-17
Category : Mathematics
ISBN : 9780521192255

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NIST Handbook of Mathematical Functions Hardback and CD-ROM by Frank W. J. Olver Pdf

The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.

Author : DK
Publisher : Penguin
Page : 711 pages
File Size : 48,9 Mb
Release : 2019-09-03
Category : Mathematics
ISBN : 9781465494207

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The Math Book by DK Pdf

See how math's infinite mysteries and beauty unfold in this captivating educational book! Discover more than 85 of the most important mathematical ideas, theorems, and proofs ever devised with this beautifully illustrated book. Get to know the great minds whose revolutionary discoveries changed our world today. You don't have to be a math genius to follow along with this book! This brilliant book is packed with short, easy-to-grasp explanations, step-by-step diagrams, and witty illustrations that play with our ideas about numbers. What is an imaginary number? Can two parallel lines ever meet? How can math help us predict the future? All will be revealed and explained in this encyclopedia of mathematics. It's as easy as 1-2-3! The Math Book tells the exciting story of how mathematical thought advanced through history. This diverse and inclusive account will have something for everybody, including the math behind world economies and espionage. This book charts the development of math around the world, from ancient mathematical ideas and inventions like prehistoric tally bones through developments in medieval and Renaissance Europe. Fast forward to today and gain insight into the recent rise of game and group theory. Delve in deeper into the history of math: - Ancient and Classical Periods 6000 BCE - 500 CE - The Middle Ages 500 - 1500 - The Renaissance 1500 - 1680 - The Enlightenment 1680 - 1800 - The 19th Century 1800 - 1900 - Modern Mathematics 1900 - Present The Series Simply Explained With over 7 million copies sold worldwide to date, The Math Book is part of the award-winning Big Ideas Simply Explained series from DK Books. It uses innovative graphics along with engaging writing to make complex subjects easier to understand.

Author : A Kundu
Publisher : CRC Press
Page : 320 pages
File Size : 43,9 Mb
Release : 2019-04-23
Category : Science
ISBN : 1420034618

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Classical and Quantum Nonlinear Integrable Systems by A Kundu Pdf

Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories

Author : Oliver Bühler
Publisher : American Mathematical Soc.
Page : 165 pages
File Size : 54,7 Mb
Release : 2006-10-12
Category : Mathematical physics
ISBN : 9780821842324

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A Brief Introduction to Classical, Statistical, and Quantum Mechanics by Oliver Bühler Pdf

This book provides a rapid overview of the basic methods and concepts in mechanics for beginning Ph.D. students and advanced undergraduates in applied mathematics or related fields. It is based on a graduate course given in 2006-07 at the Courant Institute of Mathematical Sciences. Among other topics, the book introduces Newton's law, action principles, Hamilton-Jacobi theory, geometric wave theory, analytical and numerical statistical mechanics, discrete and continuous quantum mechanics, and quantum path-integral methods. The focus is on fundamental mathematical methods that provide connections between seemingly unrelated subjects. An example is Hamilton-Jacobi theory, which appears in the calculus of variations, in Fermat's principle of classical mechanics, and in the geometric theory of dispersive wavetrains. The material is developed in a sequence of simple examples and the book can be used in a one-semester class on classical, statistical, and quantum mechanics. Some familiarity with differential equations is required but otherwise the book is self-contained. In particular, no previous knowledge of physics is assumed. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Author : Evgenij F. Miščenko
Publisher : Unknown
Page : 310 pages
File Size : 53,6 Mb
Release : 2005
Category : Chaotic behavior in systems
ISBN : UCSC:32106020204845

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Nonlinear Dynamics by Evgenij F. Miščenko Pdf

Author : Anonim
Publisher : Unknown
Page : 382 pages
File Size : 40,9 Mb
Release : 2001
Category : Measurement
ISBN : CUB:U183035340922

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Journal of Research of the National Institute of Standards and Technology by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 494 pages
File Size : 41,7 Mb
Release : 1995
Category : Functions, Special
ISBN : STANFORD:36105017336061

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Special Functions by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 500 pages
File Size : 50,9 Mb
Release : 1995
Category : Numerical analysis
ISBN : UOM:39015048180569

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Annals of Numerical Mathematics by Anonim Pdf

Author : L. Baulieu,Vladimir Kazakov,Marco Picco,Paul Windey
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 55,6 Mb
Release : 2013-12-01
Category : Science
ISBN : 9781489919199

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Low-Dimensional Applications of Quantum Field Theory by L. Baulieu,Vladimir Kazakov,Marco Picco,Paul Windey Pdf

The Cargese Summer School "Low Dimensional Applications of Quantum Field Theory" was held in July 1995. The School was dedicated to the memory of Claude Itzykson. This session focused on the recent progress in quantum field theory in two dimen sions with a particular emphasis on integrable models and applications of quantum field theory to condensed matter physics. A large fraction of the school was also devoted to a detailed review of the exciting developments in four dimensional super symmetric Yang-Mills theory. The diversity of the topics presented constitute, in our opinion, one of the most attractive features of these proceedings. Some contributions constitute a very thor ough introduction to their subject matter and should be helpful to advanced students in the field while others present entirely new research, not previously published, and should be of considerable interest to the specialist. There were in depth introductory lectures on the application of conformal field theory techniques to disordered systems, on the quantum Hall effect, on quantum in tegrable systems, on the thermodynamic Bethe Ansatz and on the new developments in supersymmetric gauges theories. The computation of the three point function of the Liouville model using conformal bootstrap methods was presented in detail.

Author : Colin Rogers
Publisher : Cambridge Scholars Publishing
Page : 166 pages
File Size : 49,8 Mb
Release : 2022-12-06
Category : Mathematics
ISBN : 9781527591554

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A Nonlinear Progress to Modern Soliton Theory by Colin Rogers Pdf

This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.

Author : Johannes Blümlein,Carsten Schneider,Peter Paule
Publisher : Springer
Page : 509 pages
File Size : 52,9 Mb
Release : 2019-02-15
Category : Computers
ISBN : 3030044793

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Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory by Johannes Blümlein,Carsten Schneider,Peter Paule Pdf

This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.