Last edited by Maugore
Saturday, July 25, 2020 | History

2 edition of Wave Equations in Higher Dimensions found in the catalog. # Wave Equations in Higher Dimensions

## by Shi-Hai Dong

Written in English

Subjects:
• Quantum theory,
• Functional equations,
• Physics

• Edition Notes

The Physical Object ID Numbers Statement by Shi-Hai Dong Contributions SpringerLink (Online service) Format [electronic resource] / Open Library OL25545358M ISBN 10 9789400719163, 9789400719170

or similarly in the higher dimensions;-Heat Equation u t= k u; (The expression is called the Laplacian and is de ned as @ 2 x + @ y + @ 2 z on R3.)-Schr odinger Equation (quantum mechanics) iu t+ u= 0;-Wave Equation u tt 2c u= 0;-Equation of oscillating rod (with one spatial variable) or . One sees in all of the examples of the chapter that the resulting ordinary differential equations are familiar and elementary to solve. The chapter analyzes Laplace's equation in three variables. The chapter gives a detailed description of the heat equation in one dimension and also studies the wave equation in one dimension.

First-Order Equations : Conservation Laws : Classification of Second-Order Equations : Wave Equation On R: : Wave Equation on an Interval : Wave Equation in Higher Dimensions : Hyperbolic Systems of First-Order Equations On the other hand, the Klein-Gordon equation with a Coulomb potential in (D+1) dimensions has been discussed by the different approaches like the large-N expansion approximate method. The purpose of this Chapter is to present the Klein-Gordon equation in arbitrary dimensions .

The 2D wave equation Separation of variables Superposition Examples Remarks: For the derivation of the wave equation from Newton’s second law, see exercise As in the one dimensional situation, the constant c has the units of velocity. It is given by c2 = τ ρ, where τ is the tension per unit length, and ρ is mass density. The.   Book Description. An Introduction to Partial Differential Equations with MATLAB ®, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat, the .

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### Wave Equations in Higher Dimensions by Shi-Hai Dong Download PDF EPUB FB2

“Wave Equations in Higher Dimensions is a well-written, comprehensive and self-contained book which is designed for graduate students and researchers in physics and mathematics. The author succeeds in fluently presenting the necessary and important material on the subject.” (Dogan Demirhan, Mathematical Reviews, June, )Cited by: Wave Equations in Higher Dimensions.

Unique compendium of the current state of research Wave Equations in Higher Dimensions book quantum wave equations in higher dimensions in the framework of non-relativistic and relativistic quantum mechanics. Usually dispatched within 3 to 5 business days. Usually dispatched within 3 to 5 business days.

Higher dimensional theories have attracted much attention because they make it Brand: Springer Netherlands. 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.

(Dogan Demirhan, Mathematical Reviews, June, )"Wave Equations in Higher Dimensions is a well-written, comprehensive and self-contained book which is designed for graduate students and researchers in physics and mathematics. The author succeeds in fluently presenting the necessary and important material on the subject.".

Free shipping for non-business customers when ordering books at De Gruyter Online. Please find details to our shipping fees here. RRP: Recommended Retail Price. Print Flyer; Overview; Content; Book Book Series. Previous chapter. Next chapter.

Wave Equation in Higher Dimensions Drábek, Pavel / Holubová, Gabriela. 30,00 € / \$ / £ Free shipping for non-business customers when ordering books at De Gruyter Online. Please find details to our shipping fees here. RRP: Recommended Retail Price.

Print Flyer; Overview; Content; Book Book Series. Next chapter. 13 Wave Equation in Higher Dimensions. 30,00 € / \$ / £ Get Access to Full Text. Citation Information. Book January the studies of the Dirac equation in higher dimensions are less than those of the Schrödinger equation case except for the works in usual three- two- and one-dimensional Author: Shi-Hai Dong.

7 Wave Equation in Higher Dimensions We now consider the initial-value problem for the wave equation in n dimensions, 8. solution of the wave equation on R3+1 plays an important role in these arguments. Consequently, a new idea was needed if one wanted to generalize these results to higher dimensions.

The missing link, apparently, was the Strichartz estimate. Its importance for nonlinear wave equations in higher dimensions had long been. The wave equation u tt= c2∇2u which models the vibrations of a string in one dimension u = u(x,t), the vibrations of a thin membrane in two dimensions u = u(x,y,t) or the pressure vibrations of an acoustic wave in air u = u(x,y,z,t).

The constant c gives the speed of propagation for the vibrations. 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 : Springer Netherlands.

Looking at this solution, which is valid for all choices (x i, t i) compatible with the wave equation, it is clear that the first two terms are simply d'Alembert's formula, as stated above as the solution of the homogeneous wave equation in one dimension.

The difference. 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. Wave Equations in Higher Dimensions: 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 Author: Shi-Hai Dong. Hence, worepresents an outgoing wave. – The wave fronts of wiare the spheres r+ct= k, contracting as time goes on.

Hence, wirepresents an incoming wave. The Cauchy Problem 1. Fundamental Solution (n=3) and Strong Huygens’ Principle. • In this section we consider the global Cauchy problem for the three-dimensional homogeneous wave equation.

For example, the two key equations that we have stud- ied are the heat equation and the wave equation. For higher dimensional problems these take the form ut= kr2u,() utt= c2r2u.() We can separate out the time dependence in each equation.

Inserting a guess of u(r,t) =f(r)T(t) into the heat and wave equations, we obtain T0f= kTr2f,(). studied are the heat equation and the wave equation. For higher di-mensional problems these take the form ut = kr2u,() utt = c2r2u.() One can ﬁrst separate out the time dependence.

Let u(r,t) = f(r)T(t). Inserting u into the heat and wave equations, we have T0f = kTr2f,() T00f = c2Tr2f.() Separating out the time and space dependence, we ﬁnd 1 k T0 T.

The 1-D Wave Equation Linear Partial Diﬀerential Equations Matthew J. Hancock Fall 1 1-D Wave Equation: Physical derivation Reference: Guenther & Lee §, Myint-U & Debnath § [Oct. 3, ] We consider a string of length l with ends ﬁxed, and rest state coinciding with x-axis.

The string is plucked into oscillation. (Dogan Demirhan, Mathematical Reviews, June, ) "Wave Equations in Higher Dimensions is a well-written, comprehensive and self-contained book which is designed for graduate students and researchers in physics and mathematics.

The author succeeds in fluently presenting the necessary and important material on the subject.". 2 Chapter 1. Elementary solutions of the classical wave equation The classical wave equation The classical Electro Magnetic eld is described by the classical Wave Equation.

A one dimensional mechanical equivalent of this equation is depicted in the gure below. A two dimensional. In Chapter 1 above we encountered the wave equation in Section and the heat equation in Section These equations occur rather frequently in applications, and are therefore often.F.

John and S. Klainerman, Almost global existence to nonlinear wave equations in three space dimensions, Comm. Pure Appl. Math., 37 (), doi: /cpa Google Scholar  F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math., 28 (), Linear Equations and Generalized Solutions Chapter 3.

The Wave Equation. The One-Dimensional Wave Equation Higher Dimensions Energy Methods Lower-order Terms Chapter 4.

The Laplace Equation. Introduction to the Laplace Equation Potential Theory and Green's Functions General Existence Theory Eigenvalues of the Laplacian Chapter 5.

The Heat Equation.