Klein gordon equation, magnetic eld, wave map equation, nonrelativisticsemiclassical limit. Water waves, sound waves and simple harmonic motion of strings are few important models of evolution equations. The klein gordon equation is a secondorder differential equation in t and thus the initial values of. Numerical solution of nonlinear kleingordon equation using. By michelle rae uy 24 january 2020 knowing how to combine pdf files isnt reserved.
Kleingordon equation for a particle in brane model. Pdf in this paper we study existence and orbital stability for solitary waves of the nonlinear kleingordon equation. It has application, for example, to relativistic fields waves. It describes the motion of spinless composite particles. The kleingordon equation in the spacetime representation 9 the quantity q2 is represented by the differential operator dalembert operator from the mass shell condition 6 this results in the kleingordon equation as the basic field equation of the scalar field. In v we discuss similar problems with klein gordon equation.
The onedimensional klein gordon equation is solved for the ptsymmetric generalized hulthen potential in the scalar coupling scheme. The text now states that this form is interpreted as the relativistic field equation for spin0 particles a and that any solution of the free dirac equation is a solution of the klein gordon equation as well b. The paint program can help you make new image files, but it cannot open document or pdf file. I paid for a pro membership specifically to enable this feature. Therefore, a system that can be described by a complex solution to the kleingordon equation also be described by a system of two independent particles with equal mass that have real solutions to the klein klein gordon equation. Klein gordon equation, hydrodynamic limits, euler equations. It is a quantized version of the relativistic energymomentum relation. So the klein gordon eld is physically and mathematically, too the simplest of the relativistic elds that one can study. Lie symmetries of kleingordon and schrodinger equations. If 1, then the limit equation is the wave map equation with one extra term coming from the magnetic eld, and the associated phase. The goal of this essay is to understand some of the mathematical and physical results arising from the einstein klein gordon equations. The exact solutions of the onedimensional klein gordon equation for the rosenmorse type potential with equal scalar and vector potentials are presented. Asymptotic properties of solutions of the nonlinear klein gordon equation. Pdf notes on the kleingordon equation researchgate.
This interpretation of the relativistic elliptical wave equation and klein. Demo cubic nonlinear kleingordon equation shenfun 3. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a pdf plugin installed and enabled in your browser. Coupled wave klein gordon equations in two and three spatial dimensions zoe wyatt university of cambridge joint with shijie dong fudan. The klein gordon equation describes a wide variety of physical phenomena such as in wave propagation in continuum mechanics and in the theoretical description of spinless particles in relativistic quantum mechanics. In chapter 2, the klein gordon equation, which describes scalar or pseudoscalar spinless particles, is derived and its analytical properties are analyzed. We now know that this is a version of the wkb quantization condition, an introduction to which is provided in notes 7. The demo is implemented in a single python file kleingordon. Consider semilinear wave and klein gordon equations w f. A new result on the kleingordon equation in the background. An oversized pdf file can be hard to send through email and may not upload onto certain file managers. Pdf solitons for the nonlinear kleingordon equation. You can nd planewave solutions to the klein gordon equation easily.
Gordon equation and dirac equation with rosenmorse potential. Kapitza spring 2018 second quantization of the klein. Exact solutions of the kleingordon equation for the rosen. It was named after oskar klein and walter gordon who proposed it to describe quantum particles in the framework of relativity. Numerical solution of nonlinear kleingordon equation. Pdf is a hugely popular format for documents simply because it is independent of the hardware or application used to create that file. Numerical solution of the nonlinear kleingordon equation. Its theoretical relevance is similar to that of the dirac equation. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. The approach is based on collocation of cubic bspline functions.
If you like you can view the klein gordon equation as a \toy model for the maxwell equations. In iv we discuss relations among green functions of w. Pdf kleingordon equation and wave function for free particle in. Ppt the klein gordon equation 1926 powerpoint presentation.
Deriving the klein gordon equation relativistic quantum. Em lorentz force derived from klein gordon s equation 11. Boundary value problems for the klein gordon equation. Optimal energy decay for the damped kleingordon equation. The klein gordon equation klein fock gordon equation or sometimes klein gordon fock equation is a relativistic wave equation, related to the schrodinger equation. In nuclear and high energy physics the study of exact solution of the klein gordon equation. Multisolitary waves for the nonlinear klein gordon equation. Numerical solution of the linear time fractional kleingordon. The emphasis is given to those elements of the formalism which can be carried on.
Mar 23, 2021 this is a demonstration of how the python module shenfun can be used to solve the timedependent, nonlinear kleingordon equation, in a triply periodic domain. Gordon kg equation is an extension of the linear wave equation with additional linear andor nonlinear terms. Klein gordon eld is characterized by \particles with rest mass mand no other structure e. Contents 1 from classical theory to quantum theory 2 quantization of real scalar eld 3 quantization of complex scalar eld 4 propagator of klein gordon eld 5 homework wei wangsjtu lectures on qft 2017. When n 2, the lie symmetries related to klein gordon equation in favor of the f. It is secondorder in space and time and manifestly lorentzcovariant. A novel method to solve nonlinear klein gordon equation arising in quantum field theory based on bessel functions and jacobian free newtonkrylov subspace methods. Relations among solutions for wave and kleingordon equations. Small amplitude generalized breathers for the klein gordon equation n.
Read on to find out just how to combine multiple pdf files on macos and windows 10. Separation of variables and exact solution of the klein. If evolution of particle in brane does not depend on brane radius then d. The plane waves 10 are basic solutions and the field 9 is constructed by. If we take the comparison between the lagrangian equation 2 and the klein gordon equation equation 16 and the conformal factor holds the conditions ij 0,for some important functions ckv or kv or hv, then we analyze the following conclusion. Particles and antiparticles, two component framework. The klein gordon equation does not form the basis of a consistent quantum relativistic oneparticle. Local smooth solutions of the nonlinear kleingordon equation. Kleingordon equation spline collocation methods for. In order to introduce relativistic corrections in a nonperturbative way, one should solve the klein gordon equation or dirac equation for the particle in the. Klein gordon equation relativistic description of quantum theory once upon a time, many physicists tried to nd the equation that is both relativistic and quantum at once. The klein gordon equation gave negative probabilities and this is considered to be physically meaningless.
An approach tothekleingordon equation for a dynamic study in. In paper 8 the nonlinear onedimensional klein gordon equation was solved with the help of the. The klein gordon equation plays an important role in mathematical physics. Bound states of the kleingordon equation with vector. Numerical solution of the kleingordon equation in an. Recently, the dissipative form of this equation turned out to be a fundamental. Analysis and comparison of numerical methods for the klein. It has root coming from the study of theoretical physics with importance in quantum mechanics. The eld equation known as the klein gordon equation is given by m2 0.
The homotopy perturbation method hpm has been successively applied for finding approximate analytical solutions of the fractional nonlinear kleingordon equation which can be used as a numerical algorithm. Adobe systems is a software manufacturer that has created many document and multimedia editing programs. Falaye 8, solved the klein gordon equation with ringshaped potentials. Relations among solutions for wave and kleingordon. For some of the potentials we use the lie admitted symmetries to determine the corresponding invariant solution of the klein gordon equation. The klein gordon equation arises in relativistic physics such as cosmology and in general. Di erential equations 2014 proves the existence of breathers with exponentially small tails. Hydrodynamic limits of the nonlinear kleingordon equation. Based on this result we develop a numerical method for solving the cauchy problem and test its performance. Mae 105 introduction to mathematical physics homework 6 solution problem 1. The operator is named after french mathematician and physicist jean le rond dalembert in minkowski space, in standard coordinates t, x, y, z, it has the form. This means it can be viewed across multiple devices, regardless of the underlying operating system.
This article explains what pdfs are, how to open one, all the different ways. Luckily, there are lots of free and paid tools that can compress a pdf file in just a few easy steps. Coupled wave kleingordon equations in two and three. The klein gordon equation 21 is completely separable in 3, therefore we look for its solution in the form. Convergence of the kleingordon equation to the wave map. Wang, a compact difference scheme for a two dimensional fractional klein gordon equation with neumann boundary conditions, entropy, 274 2014, 268282. Chapter 11 em lorentz force derived from klein gordons. I go over fourvector notation, fourgradient, and writing the equ. In special relativity, electromagnetism and wave theory, the dalembert operator denoted by a box. You can use the tools in paint to add something to a different document. Due to the large number of cases and for easy reference the results are presented in the form of tables. On timesplitting pseudospectral discretization for. Numerical solution of nonlinear system of kleingordon. Kleingordon equation where the integral is taken around a closed classical orbit, would imply that there was an integral number of wavelengths along the quantized orbits.
The existence of global weak solutions has been obtained by jorgens 2, pecher 3. The late sidney coleman taught the quantum field theory course at harvard for many years, influencing a generation of physicists in the way they view and teach qft. A pdf file is a portable document format file, developed by adobe systems. The kleingordon equation is solved using a mixed formulation. Bohrsommerfeld semiclassical solution of the coulomb problem, the dirac equation and the clifford algebra. This method not very well known and used is of great importance in the scienti. Relativistic wave equations are invariant under lorentz transformations, expressing the invariance of the element of 4vector length, ds 2 dt 2. The pdf format allows you to create documents in countless applications and share them with others for viewing. Klein gordon eld the simplest relativistic classical eld is the klein gordon eld. Below you can find the pdf files of handwritten lecture notes for colemans course transcribed by brian hill. Dispersive wave solutions of the kleingordon equation in.
The klein gordon equation or klein fock gordon equation is a relativistic version of the schr. A numerical method based on collocation points was developed in 7 to solve the nonlinear klein gordon equations by using the taylor matrix method. The klein gordon equation was historically rejected as a fundamental quantum equation because it predicted negative probability density. The kleingordon equation in curved spacetime from within the proper time formalism of schwinger and dewitt has been treated, at least from the gaussian approximation, by beken stein 2, 3. Its solutions include a quantum scalar or pseudoscalar field, a field whose. The klein gordon equation is a relativistic wave equation, related to the schrodinger equation. Indeed, one of the most fundamental questions that should be asked when studying these equations is whether the solution if it exist goes.
Equation 12 is of course the relativistic energymomentum relation all. The klein gordon equation applying to the relativistic equation for energy. Numerical technique for solving kleingordon equation with. Coupling to electromagnetism, solution of the coulomb problem. The hydrodynamical structures and the formal analysis is referred to 6. A pdf portable document format is a widely popular type of document format created by adobe. Communications in partial differential equations, vol. Kapitza spring 2018 second quantization of the kleingordon. Ikhdair and hamzavi 9, investigated the effects of external fields on a twodimensional klein gordon equation of a particle under pseudoharmonic oscillator interaction. Small generalized breathers with exponentially small tails for klein gordon equations. In a suitable approximation it is shown that for the linear potential which is of interest in quark interactions, their con.
Therefore, as long as energy and momentum follows the einsteins relation eq. Making a pdf file of a logo is surprisingly easy and is essential for most web designers. Once youve done it, youll be able to easily send the logos you create to clients, make them available for download, or attach them to emails in a fo. The klein gordon equation becomes, means that it is sensible to the smallness of the em coupling, make a perturbation expansion of v in powers of 4 physical interpretation of quantum mechanical equations schrodinger equation s. An introduction to miniboson stars, including reference to numer. The homotopy perturbation method hpm has been successively applied for. Boundstate solutions of the kleingordon equation for the. To make a comparison between numerical solutions and analytical ones, four klein gor don equations with quadratic or cubic nonlinearity are considered. Non existence of small amplitude breathers for klein. To read the file of this research, you can request a copy directly from the authors. The local equilibrium distribution function and the amending function are obtained.
A technique to approximate the solutions of nonlinear klein gordon equation and klein gordon schrodinger equations is presented separately. How to use the einstein energymomentum relation to derive the klein gordon wave equation. Solutions of the klein gordon equation with generalized. That is where cryptohermitian approach can be applied.
One of the fun things about computers is playing with programs like paint. Boundstate solutions of the kleingordon equation with. The radial part of the kleingordon equation in for special case is written as substituting into, we obtain obviously, this equation cannot be solved analytically for due to the centrifugal term. In this paper, we make free particles wave function as the solution of klein gordon equation in rindler spacetime. Searching for a specific type of document on the internet is sometimes like looking for a needle in a haystack. How to shrink a pdf file that is too large techwalla.
Due to the runge approximation theorem any harmonic in function can be approximated uniformly on any compact subset inside by harmonic polynomials. The klein gordon equation is a relativistic version of the schrodinger equation. Approximate analytical solutions of the effective mass. As a consequence, we also arrive at a purely operator theoretic proof of the wellposedness of the initial value problem of the reduced normalized klein gordon equation in the gravitational. Solving the fractional nonlinear kleingordon equation by. Sep 23, 2019 the klein gordon equation with a scalar potential and a vector potential in ddimensions reads where represents the spatial dimensionality and represents the laplace operator in ddimensions, is the reduced planck constant, and are the speed of light and relativistic energy of the system, respectively. To begin with we can think of the klein gordon eld as simply a function on spacetime, also known as a scalar eld. Such models arise from delay differential equations and partial differential equations in many disciplines including physics, chemistry, biology, engineering, and economics. Pdf file or convert a pdf file to docx, jpg, or other file format.
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