Wave Equations in Higher Dimensions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Wave Equations in Higher Dimensions write by Shi-Hai Dong. This book was released on 2011-07-09. Wave Equations in Higher Dimensions available in PDF, EPUB and Kindle. Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativistic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem and the generalized hypervirial theorem in higher dimensions, the Schrödinger equation with position-dependent mass and the Kaluza-Klein theory in higher dimensions are investigated. In this context, the dependence of the energy levels on the dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography.
Two Exterior Goursat Problems of the Wave Equation in Higher Dimensions
Two Exterior Goursat Problems of the Wave Equation in Higher Dimensions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Two Exterior Goursat Problems of the Wave Equation in Higher Dimensions write by Jeou-Hwa Wang. This book was released on 1970. Two Exterior Goursat Problems of the Wave Equation in Higher Dimensions available in PDF, EPUB and Kindle.
Higher-Order Numerical Methods for Transient Wave Equations
Higher-Order Numerical Methods for Transient Wave Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Higher-Order Numerical Methods for Transient Wave Equations write by Gary Cohen. This book was released on 2001-11-06. Higher-Order Numerical Methods for Transient Wave Equations available in PDF, EPUB and Kindle. "To my knowledge [this] is the first book to address specifically the use of high-order discretizations in the time domain to solve wave equations. [...] I recommend the book for its clear and cogent coverage of the material selected by its author." --Physics Today, March 2003
Nonlinear Wave Equations
Nonlinear Wave Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Wave Equations write by Walter A. Strauss. This book was released on 1990-01-12. Nonlinear Wave Equations available in PDF, EPUB and Kindle. The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.
Finite Difference Computing with PDEs
Finite Difference Computing with PDEs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Difference Computing with PDEs write by Hans Petter Langtangen. This book was released on 2017-06-21. Finite Difference Computing with PDEs available in PDF, EPUB and Kindle. This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.
