Klein gordon equation

klein gordon equation Back to Contents. The book "Advanced Visual Quantum Mechanics" by Thaller includes Mathematica software packages for the numerical solution of the Klein-Gordon equation and the Dirac equation (subject to user-defined The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic version of the Schrödinger equation. It Fourier uniqueness sets and the Klein-Gordon equation 3 We should understand the invariance properties of local Heisenberg uniqueness pairs with DEPT. ii. H is hermitian if , but The square root leads to an infinite number of try is a nonlocal symmetry in both cases of Klein Gordon equation. Finding exact solutions to this equations provides importan informationabout the behavior 3 Numerical treatment of coupled nonlinear hyperbolic Klein-Gordon equations 249 Legendre, Chebyshev and Gegenbauer polynomials [44–46]. It should be noted that cubic nonlinear Klein-Gordon equations in one space dimension are of special interest, because the large-time behavior of the solution is actually affected by the structure of the nonlinearities, even if the data are sufficiently small, smooth and We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small analytic norm remain small for exponentially long times. A wave equation describing a spinless particle which is consistent with the special theory of relativity. /CMA UNIVERSITY OF OSLO PURE MATHEMATICS NO 17 ISSN 0806–3842 J UNE 2008 Solving the Maxwell-Klein-Gordon equation in the Lattice Gauge Theory formalism Snorre H. It is a quantized version of the relativistic energy October 15, 2008 8:56 WSPC/141-IJMPC 01292 Exact Bound States of the D-Dimensional Klein{Gordon Equation 1427 The radial and angular parts of the Klein{Gordon equation with this type of po- To find the Klein-Gordon equation for a spin zero particle interacting with an electro-magnetic field, replace ∂ µ by ∂ µ + iqA µ where qis the charge of the particle,A µ is the isthe four dimensional vectorpotential. So the K-G equation does not necessarily represent particles with non-zero spin. Also known as Schrödinger-Klein-Gordon equation. The Klein-Gordon Equation may be considered as acceleration. There has been a growing interest in investigating the approximate solutions of the Klein-Gordon equation and relativistic wave equations for some physical potential mode. . The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. 1. , 21 (1990), 1190-1212 Theorem 5. It would be very useful 2 Nonlinear Klein-Gordon equations EJDE{2002/26 The interaction of with the electro-magnetic eld is described by the min-imal coupling rule, that is the formal substitution The Klein-Gordon equation describes how the state of a relativistic (= fast moving) quantum system without spin changes in time. Energy heuristics predict global existence from small data for semi-linear Klein-Gordon In this paper, the homotopy analysis method is applied to obtain the solution of nonlinear fractional partial differential equations. ON RETARDED GREEN'S FUNCTION FO R COVARIANT KLEIN-GORDON EQUATION R. P. 1 DERIVATION AND COVARIANCE The requirements which special relativity imposes upon quantum mechanics are both fascinating and far View Klein-Gordon equation Research Papers on Academia. 2096v1 [math-ph] 13 Nov 2008. , 21 (1990), 1190-1212 The PowerPoint PPT presentation: "Relativistic QM The Klein Gordon equation 1926" is the property of its rightful owner. Biler, Attractors for the system of Schrödinger and Klein-Gordon equations with Yukawa Coupling, SIAM J. EXACT SOLUTIONS OF THE KLEIN-GORDON EQUATION WITH HYLLERAAS POTENTIAL Akpan N. Awoga1 and Benedict I. 2 Dirac Equation Dirac(1928) want to construct a relativistic wave equation –rst order in time derivative just like Schrodinger equation which has conserved probabilty and positive. Get PDF (687K) More content like this. We consider the initial-value problem for the Klein-Gordon equa- Klein-Gordon Equation The scalar wave equation is appropriate for a spin zero particle, a charged 1T meson, for example. 2 Another Example: First Order The non relativistic limit of the Klein-Gordon equation (K-G) is the Schrodinger equation (S). The Klein–Gordon equation is a relativistic wave equation, related to the Schrödinger equation. Klein Gordon Equation F or a free relativistic particle the total energy E is no longer giv en b y the equation w e used to deriv e the Sc hro edinger equation. The approximate analytical solution of the A sharp bilinear estimate for the Klein--Gordon equation in arbitrary space-time dimensions Jeavons, Chris, Differential and Integral Equations, 2014 Scattering theory for the coupled Klein-Gordon-Schrödinger equations in two space dimensions II SHIMOMURA, Akihiro, Hokkaido Mathematical Journal, 2005 Despite the name, the Maxwell-Klein-Gordon equation is not really related to the (massive) Klein-Gordon equation. . We use these fundamental solutions to represent I have a sound grounding on ODE's, not that much on PDE's, i've read many books on QFT and most if not all come to the conclusion that the solution to the Klein-Gordon equation $$(\partial_{\mu}\pa There has been a growing interest in investigating the approximate solutions of the Klein-Gordon equation and relativistic wave equations for some physical potential mode. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the usual Schrödinger equation. Tahmina Akter et al. Honda, a former student of Dr. The Klein–Gordon equation is a relativistic version of the Schrödinger equation. edu for free. The Klein-Gordon Equation; Addendum. com. Moreover, we organize a strong relationship among the Lie symmetries related to Klein-Gordon as Klein-Gordon equation (5) is the master equation for the ultra-short thermal phe- nomena with finite transport speed . 105, 171{191, 2010 DERIVATION OF KLEIN-GORDON EQUATION FROM MAXWELL’S EQUATIONS AND STUDY OF RELATIVIS- Klein-Gordon’s equation We consider the scalar field φ(x) which, according to its definition, behaves under Lorentz transformation like φ0(x0) = φ(x). Components of the vector may also repres Abstract In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. The negative energy solution of Klein-Gordon equation has a strange property that the energy decreases as the magnitude of the momentum increases. It is second order in space and time and manifestly Lorentz covariant . Naumkin, A bilinear estimate and its application to a quadratic nonlinear Klein–Gordon equation in two space dimensions, Journal of Functional Analysis, 2016, 270, 6, 1971CrossRef THE KLEIN-GORDON EQUATION VI. The infor-mation of Lie point symmetries of Klein Gordon equation and Schrödinger equ- Klein-Gordon equation (1. Ita 2 1 Theoretical Physics Group, Department of Physics, University of Uyo-Nigeria. The Klein–Gordon equation for the complex scalar field is the relativistic ver-sion of the Schrödinger equation, which is used to describe spinless particles. Math. This equation appears in relativistic physics and is For wave equations (the statements in the following do not apply as well to the Klein-Gordon equations for technical and not-completely understood reasons) there is a third natural notion of infinity, which is that of null or light-like infinity. The potential consist of the Harmonic oscillator potential plus a novel The Dirac equation, on the other hand, was an attempt by Dirac to factorize the Klein Gordon equation to make the equation contain only first-order derivatives in space and time so that the resulting probability current is positive definite. Mankin, A. Asymptotic Completeness. 3-1. www. Historically A generalized series is used to obtain bounded solutions of the Klein Gordon equation using the Frobenius method. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta Chapter 9 Relativistic matter waves from Klein Gordon’s equation from my book: Understanding Relativistic Quantum Field Theory Hans de Vries November 10, 2008 Classical Field Theory The Klein-Gordon eld and its variational principle. The quasilinear Klein-Gordon equation is given by I am being really thick here I have this wave equation, the massless klien gordon equation \partial_{\mu}\partial^{\mu}\phi(x)=0 where the summation Chapter 3 The Klein-Gordon Equation 3. Using the NU method, we obtain try is a nonlocal symmetry in both cases of Klein Gordon equation. Now Introduction to Relativistic Quantum Mechanics The Wave Function The Klein-Gordon Equation Connection to the Maxwell Equations Implications. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta Invariance of the Klein-Gordon equation under time-reversal transformation: (76) since it is a differential equation of second order in t. The wave equation is found by taking the 1 Lecture 31: Introduction to Klein-Gordon Equation Physics 452 Justin Peatross 31. 22) is consistent with all the classical dynamics (1). This feature is not available right now. The Klein-Gordon Equation is a relativistic generalisation of the Schrordinger Equation to Relativistic Quantum Mechanics. Quantum mechanics Uncertainty principle. Using this method, wave functions and corresponding exact energy equation In the thesis we will discuss some recent developments for a particular semi-linear defocusing wave equation: the semilinear ujujp 1 Klein-Gordon equation, focusing on the two and three space dimensions cases. Klein-Gordon Equations, the thesis of Dr. Why can't the Schrödinger equation be solved exactly for multi-electron atoms? Does some solution exist even in principle? How to identify or authorize members of a time travel organisation? An acceleration field may be represented as a vector. IntroductionThe nonlinear Klein–Gordon equation arises in various problems in science and engineering. For some examples used, we obtain similar results to that using Nikiforov Uvarov method (NU). Ikot+1, Oladunjoye A. They are used to characterize and estimate eigenvalues in cases where the essential spectrum has a gap around 0, even in the presence of complex eigenvalues. The solutions are based on the physical principle of maintaining local gauge invariance in the Furry picture Lagrangian when N external fields can undergo independent gauge transformations. 2 - Complex Scalar Field Obeying Klein-Gordon Equation Nicola Canzano Physics Dept. Nov 13, 2008 - arXiv:0811. Please try again later. Rather, it is the Maxwell equation coupled with a massless scalar equation (i. Progress In Electromagnetics Research, Vol. However, as | a |→0 (where superradiance is weaker and one expects the problem to transactions of the american mathematical society Volume 290, Number 2. The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic version of the Schrödinger equation. Introduction to Relativistic Quantum Mechanics The Wave Function The Klein-Gordon Equation Connection to the Maxwell Equations Implications. com EN. e. Matthew W. Perturbed Klein-Gordon Equation. 2. OF MATH. In the relativists' language this is the space-time boundary portion usually denoted $\mathscr{I}^\pm$. In this paper, we propose a numerical scheme to solve the one-dimensional nonlinear Klein–Gordon equation with quadratic and cubic nonlinearity. The solution of the radial Klein-Gordon equation for the Hulth´en potentials with an arbitrary angular momentum = 0 are obtained. Christiansen∗ and Tore Gunnar Halvorsen† The Finite Difference Methods for –Nonlinear Klein Gordon Equation www. Klein–Gordon equation What is the Lagrangian from which the Klein-Gordon equation is derived in QFT? How to obtain Dirac equation from Schrodinger equation and special relativity? DEPT. The Chebyshev Collection Method for Solving Fractional Order Klein-Gordon Equation M. 1 Ph ysical Problems of the Klein-Gordon Equation The Klein-Gordon equation (2. H is hermitian if , but The square root leads to an infinite number of Klein–Gordon equation. 2 (propagation of general solutions of the Klein-Gordon equation) Let denote the mean value of on the sphere , and let be the derivative of with respect to . An approximate solution of the Klein–Gordon equation for the general Hulthén-type potentials in D-dimensions within the framework of an approximation to the centrifugal term is obtained. a free wave equation). KLEIN-GORDON EQUATION IN SCHRÖDINGER FORM 3 which is the usual relativistic formula for the energy of a particle. Abstract: In this article we construct the fundamental solutions for the Klein-Gordon equation in de Sitter spacetime. Ethan P. Now HW 2, No. Different from all other Definitions of Klein-Gordon equation, synonyms, antonyms, derivatives of Klein-Gordon equation, analogical dictionary of Klein-Gordon equation (English) Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 1 Review of De Broglie - Schrödinger From the de Broglie relation, it is possible to ‘derive’ the Schrödinger equation, at least in In the present paper, we couple double Laplace transform with Iterative method to solve nonlinear Klein-Gordon equation subject to initial and boundary conditions. a relativistic (that is satisfying the requirements of the theory of relativity) quantum equation for particles with zero spin. Strictly as per the compliance and regulations of : Klein-Gordon Equation for a Particle in Brane 26 M. KHADER Faculty of Science, Benha University Department of Mathematics Free Klein-Gordon Equation. iosrjen. Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow. In classical physics we seek to describe motion. The analogous equation for systems with half-integer spin is the Dirac Equation . Choptuik. By this method noise terms disappear in the iteration process and single iteration gives the exact solution. We establish local and global existence results for Dirac- Numerical Solution of Fractional Diffusion Wave Equation and Fractional Klein–Gordon Equation via Two-Dimensional Genocchi Polynomials with a Ritz–Galerkin Method. The Dirac Equation The Hydrogen Atom Why do we need the Dirac Equation? The mathematical Formalism Klein-Gordon equation Dirac equation Schr¨odinger Equation and Lorentz Transformation 5 The Dirac Equation and Spinors The problems with the Klein-Gordon equation led Dirac to search for an alternative relativistic wave equation in 1928, in which Low Regularity Solutions for Dirac-Klein-Gordon Equations in one Space Dimension Yung-fu Fang Abstract. 2 Nonlinear Klein-Gordon equations EJDE{2002/26 The interaction of with the electro-magnetic eld is described by the min-imal coupling rule, that is the formal substitution Solving the Klein-Gordon equation using fourier spectral methods: a benchmark test for computer performance the Klein–Gordon equation decays faster than the wave equation on Minkowski space, one may have expected that the Klein–Gordon equation would be easier to control. , in the presence of a source. A complex field remains a complex field as expected for non-relativistic problems (where we are all familiar with wave functions and their interpretation). We establish local and global existence results for Dirac- In this paper, the homotopy analysis method is applied to obtain the solution of nonlinear fractional partial differential equations. i. 3 is itself incapa Generalizing the Klein-Gordon equation Kevin Gibson August 16, 2010 Introduction The Klein-Gordon equation can be expressed as follows1 ∇2 − 1 c2 ∂2 ∂t2 E0 cℏ 2 The Klein-Gordon equation plays a significant role in mathematical physics and many scientific applications such as solid-state physics, nonlinear optics, and quantum field theory [1]. Klein-Gordon Fields in Curved Spacetimes and Other Backgrounds : Beyer et al GRG(13)-a1206 [stability of solutions of the Klein-Gordon equation]; Burko We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small analytic norm remain small for exponentially long times. In this paper we construct a parametrix for the forward fundamental solution It is shown that solutions of the nonlinear Klein-Gordon equation u tt - ∆ u + mu + P '( u ) = 0 decay to zero in the local L 2 mean if the initial energy is bounded provided s P ') s ) - 2 P ( s ) ≥ a P ( s ) ≥ 0 with a > 0. Free Klein-Gordon Equation. Historically The Klein-Gordon equation is derived. enacademic. that arises in mathematical physics. , Differential and Integral Equations, 2016 Generalized energy conservation for Klein--Gordon type equations Böhme, Christiane and Hirosawa, Fumihiko, Osaka Journal of Mathematics, 2012 Math 53: Chaos! Stability Analysis of Spherically Symmetric Solutions to the Klein Gordon Equation Luis Martinez November23,2015 1 Introduction Klein-Gordon equation is local and manifestly Lorentz covariant. Although the Green's function of the Klein-Gordon equation is given (precomputed as an example) on the DiracDelta and HeavisideTheta functions documentation pages, Mathematica 11. 81) Suppose one is interested in obtaining solutions to the inhomogeneous Klein- Gordon (KG) equation i. 1. We consider three examples of vibrating systems whose mathematical descriptions lead to the Klein–Gordon equation. The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. The method has been successively provided for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation. It has been used to solve effectively, easily The cubic Klein-Gordon equation is a simple but non-trivial partial differential equation whose numerical solution has the main building blocks required for the solution of many other partial differential equations. A PARAMETRIX FOR THE FUNDAMENTAL SOLUTION OF THE KLEIN-GORDON EQUATION ON ASYMPTOTICALLY DE SITTER SPACES DEAN BASKIN Abstract. The Klein–Gordon equation is a linear homogeneous second-order partial differential equation with constant coefficients: (1) where is a (pseudo-) scalar function, in the general case — complex, and is the rest mass of the particle. The potential consist of the Harmonic oscillator potential plus a novel applied to solve various forms of nonlinear Klein-Gordon type equations. It is the equation of motion of a quantum scalar or pseudoscalar field The solution of the radial Klein-Gordon equation for the Hulth´en potentials with an arbitrary angular momentum = 0 are obtained. Thus there is a need to find a new quantum equation that accounts for rest mass energy, beside Abstract In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In Chapter 2, the the Klein-Gordon equation By Haakan Hedenmalm and Alfonso Montes-Rodr guez Abstract A Heisenberg uniqueness pair (HUP) is a pair ( ;), where is a curve 24"x36" Standard Canvas Iridescent Paint & 18k Gold Paint Black Floating Frame "In solving practical problems in science and engineering arises as a direct consequence differential equations that explains the dynamics of the phenomena. In Quantum Field Theory, it is a relativistic field equation for a spin-0 field (Klein-Gordon Field). 2). We also review some existing results of them and report our main results. The infor-mation of Lie point symmetries of Klein Gordon equation and Schrödinger equ- Finally, combining the two rst-order (in @=@t) equations (15) and (24) for the quantum elds ˚^ and ^ˇwe obtain the quantum version of the Klein{Gordon equation, @ 2 The hydrogenic Klein Gordon equation in the coordinate representation is , (1) The energy eigenvalues are , , (2) where Z is the atomic number By employing the static (one-dimensional) Klein-Gordon equation, we have performed a theoretical analysis to show that the behaviour of a single photon in a semi-infinite waveguide is equivalent to photon quantum tunneling. P. The application of differential transform method is extended to derive approximate analytical solutions of nonlinear Klein-Gordon type equations. August 1985 UNSTABLE GROUND STATE OF NONLINEAR KLEIN-GORDON EQUATIONS The Method of Multiple Scales for nonlinear Klein-Gordon and Schrodinger Equations¨ Diploma Thesis of Patrick Kramer¨ Duration: 06. The Klein-Gordon (KG) Scalar Relativistic Wave Equation [] {\mathbf Remarks:} The KG-equation is a Lorentz invariant expression. Particular solutions of the Klein–Gordon equation: w The quantum mechanical origin of the Klein–Gordon equation hides its capability to model many classical systems. This paper is devoted to the numerical solution of an one-dimensional nonlinear Klein–Gordon equation, which is given in the following form: Klein-Gordon Equation The existence of plane waves φ(r, t) exp(ik r iωt) satisfying de Broglie and Einstein relations p = k, E = ω implies the quantum operator interpretation p i, E i t. Anal. For specific computations of specific cases it can only be utilized with the appropriate boundary conditions. In this paper variational principles for eigenvalues of an abstract model of the Klein–Gordon equation with electromagnetic potential are established. The linear Klein-Gordon equation occurs as a modification of the linear Schrödinger equation that is consistent with special relativity, see for example Landau We present the analytical solutions of the Klein-Gordon equation for q-deformed equal vector and scalar Eckart potential for arbitrary -state. org 2 | P a g e describes, for example, structural phase transitions in ferroelectric and ferromagnetic materials, topological We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ. It will be proven that Klein-Gordon and Dirac equation, when Equation (5) was given to us by Dirac, where ~ is called the Dirac constant, and ω is the angular frequency of the orbiting photons about a fixed point in space. It is second order in space and time and manifestly Lorentz covariant. The time-dependent form is where is the d'Alembertian , is the wavefunction , m is the mass of the particle, c is the speed of light , and is h-bar . Using the NU method, we obtain The Klein-Gordon equation (KGE) that is known as the Schr¨odinger’s relativistic wave equation is one of the most important mathematical models in quantum field theory [1–14]. In 1925, shortly after Louis deBroglie asserted the wave-particle duality for matter and just a little short of a quarter century after Max Planck asserted the same duality for electromagnetic radiation, Erwin Schrödinger devised and presented an equation familiar to all students of modern physics. Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The relativistic quantum mechanic equation for a free particle is the Klein-Gordon equation (h=c=1) Every Solution of the Dirac Equation is also a solution of the Klein-Gordon equation. , University of California, Santa Cruz October 18, 2015 Keywords and phrases: Klein-Gordon equation, hydrodynamic limits, Euler equations. Christiansen∗ and Tore Gunnar Halvorsen† Green Functionsfor the Klein-Gordon operator(v0. The problem with the Klein-Gordon equation is that it does not incorporate spin and thus will only work for spinless particles. 1 DERIVATION AND COVARIANCE The requirements which special relativity imposes upon quantum mechanics are both fascinating and far Klein-Gordon and Dirac Equations The Klein-Gordon and Dirac equations are analogs of the Schrodinger equation which try to make quantum me-chanics compatible with special relativity unlike the Schrodinger equation which is compatible only with Galilean The Klein–Gordon equation is encountered in quantum field theory and a number of applications. Components of the vector may also repres We follow and modify the Feshbach-Villars formalism by separating the Klein-Gordon equation into two coupled time-dependent Schroedinger equations for particle the Klein-Gordon equation and the Klein-Gordon-Schr˜odinger equations. 1 Review of De Broglie - Schrödinger From the de Broglie relation, it is possible to ‘derive’ the Schrödinger equation, at least in Although the Green's function of the Klein-Gordon equation is given (precomputed as an example) on the DiracDelta and HeavisideTheta functions documentation pages, Mathematica 11. In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. We obtain the energy spectrum and the corresponding unnormalized wave function expressed in terms of the Jacobi polynomial. The non relativistic limit of the Klein-Gordon equation (K-G) is the Schrodinger equation (S). 1 An Example: The Klein-Gordon Equation 8 1. : Variational Iteration Method for Solving Coupled Schrödinger-Klein-Gordon Equation errors is avoided. Choptuik is a professor in the Department of Physics The Finite Difference Methods for –Nonlinear Klein Gordon Equation www. Choptuik is a professor in the Department of Physics There is a minor study on the nonstandard finite difference method for Klein-Gordon equation. First, we briefly review Nikiforov–Uvarov mathematical method. Particular solutions of the Klein–Gordon equation: w The Klein-Gordon equation is an equation of mathematical physics that describes spin-0 particles. In this paper, the solutions of the Klein-Gordon equation for a di- atomic molecule in a non-central potential are investigated analytically. This paper is devoted to the numerical solution of an one-dimensional nonlinear Klein–Gordon equation, which is given in the following form: It is shown that solutions of the nonlinear Klein-Gordon equation u tt - ∆ u + mu + P '( u ) = 0 decay to zero in the local L 2 mean if the initial energy is bounded provided s P ') s ) - 2 P ( s ) ≥ a P ( s ) ≥ 0 with a > 0. Find more content: like this article; In this post, we introduce some recent works to the single nonlinear Klein-Gordon equations in one space dimension. A. It can describe the thermal energy propagation in The book "Advanced Visual Quantum Mechanics" by Thaller includes Mathematica software packages for the numerical solution of the Klein-Gordon equation and the Dirac equation (subject to user-defined For wave equations (the statements in the following do not apply as well to the Klein-Gordon equations for technical and not-completely understood reasons) there is a third natural notion of infinity, which is that of null or light-like infinity. Find more content: like this article; Klein-Gordon Equation for a Particle in Brane Model. Naumkin, A bilinear estimate and its application to a quadratic nonlinear Klein–Gordon equation in two space dimensions, Journal of Functional Analysis, 2016, 270, 6, 1971CrossRef In/Equivalence of Klein-Gordon and Dirac Equation Hans Detlef Hutten¨ bach Abstract. 1 Introduction In this paper, we study the nonlinear Klein-Gordon equation In this paper, the solutions of the Klein-Gordon equation for a di- atomic molecule in a non-central potential are investigated analytically. 14 The Klein-Gor­don equa­tion The Schrö­din­ger equa­tion for the quan­tum wave func­tion is based on the non­rel­a­tivis­tic ex­pres­sion for the en­ergy of a par­ti­cle. The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second order in Abstract— Reduced differential transform method (RDTM) is implemented for solving the linear and nonlinear Klein Gordon equations. In this paper, we implement the nonstandard finite difference method that is incorporated with harmonic mean averaging to approximate the known function that appears in inhomogeneous Klein- P. It is a quantized version of the relativistic energy Introduction to Elementary Particle Physics. It is given by: It is given by: ⁢ ψ = ( m ⁢ c ℏ ) 2 ⁢ ψ THE KLEIN-GORDON EQUATION VI. Suppose that is a smooth solution of the Klein-Gordon equation (3. Lecture 15 Page 1 of 6 Relativistic Quantum Mechanics • Klein-Gordon Equation Invariance of the Klein-Gordon equation under time-reversal transformation: (76) since it is a differential equation of second order in t. 70 it is shown that each component of the vector Y in 9 satisfies the The Klein-Gordon equation is the linear partial differential equation which is the equation of motion of a free scalar field of possibly non-vanishing mass m m on some (possibly curved) spacetime (Lorentzian manifold): it is the relativistic wave equation with inhomogenety the mass m 2 m^2. The bound state energy eigenvalues and the normalized eigenfunctions are obtained in terms of hypergeometric Low Regularity Solutions for Dirac-Klein-Gordon Equations in one Space Dimension Yung-fu Fang Abstract. 24"x36" Standard Canvas Iridescent Paint & 18k Gold Paint Black Floating Frame the Klein-Gordon equation By Haakan Hedenmalm and Alfonso Montes-Rodr guez Abstract A Heisenberg uniqueness pair (HUP) is a pair ( ;), where is a curve Klein–Gordon equation: Download this page on PDF Part of a series of articles about: Quantum mechanics The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic version of the Schrödinger equation. Sauga It is shown that, in case of special classes of static metrics, the fundamental solution In this paper, we investigate the Lie point symmetries of Klein-Gordon equation and Schr?dinger equation by applying the geometric concept of Noether point symmetries for the below defined Lagrangian. In Greiner’s eqn 1. The solutions of our mo del equations are calculated in the form of convergent Klein-Gordon’s equation We consider the scalar field φ(x) which, according to its definition, behaves under Lorentz transformation like φ0(x0) = φ(x). Klein-Gordon Equation for a Particle in Brane Model. 1 Inner Product As we learned in the lecture 31, the Klein-Gordon equation is more general than the 1 Nakao Hayashi, Pavel I. 70 it is shown that each component of the vector Y in 9 satisfies the The nonlinear Klein–Gordon equation is used to model many nonlinear phenomena. Approximate Analytical Solutions of the Klein-Gordon Equation fo An acceleration field may be represented as a vector. 66) ful lls the la ws of sp ecial relativit y, but Classical Field Theory The Klein-Gordon eld and its variational principle. equation is not completely destroyed in the quantum eld theoretic picture, however. RU; DE; FR; ES; Remember this site; Embed dictionaries into your website An equation which hold for spinless particles. SMALL DATA BLOW-UP FOR SEMILINEAR KLEIN-GORDON EQUATIONS By MARKUS KEEL and TERENCE TAO Abstract. The Klein-Gordon equation for a function defined on the Schwartz Space over the Minkowski Spacetime is: (1) where is the box-operator or the D’Alembertian with respect to the -coordinate ( ). The Klein-Gordon Equation Meets the Cauchy Horizon Itai Seggev Enrico Fermi Institute and Department of Physics University of Chicago University of Mississippi A generalized series is used to obtain bounded solutions of the Klein Gordon equation using the Frobenius method. Using equations of motion, we calculate descriptions of trajectories followed by particles and bodies. 80 likes. Approximate Analytical Solutions of the Klein-Gordon Equation fo 5 The Dirac Equation and Spinors The problems with the Klein-Gordon equation led Dirac to search for an alternative relativistic wave equation in 1928, in which The Klein-Gordon equations appear in quantum field theory, relativistic physics, dispersive wave-phenomena, plasma physics , nonlinear optics and applied and physical sciences [1, 13, 28] and are of the form On contrary Klein-Gordon equation can account for rest mass energy but does not have potential energy term for fields other than electromagnetic fields. The relativistic quantum mechanic equation for a free particle is the Klein-Gordon equation (h=c=1) Klein-Gordon Equation The existence of plane waves φ(r, t) exp(ik r iωt) satisfying de Broglie and Einstein relations p = k, E = ω implies the quantum operator interpretation p i, E i t. RU; DE; FR; ES; Remember this site; Embed dictionaries into your website 1 Lecture 32: Klein-Gordon Equation – Wave Packet Construction Physics 452 Justin Peatross 32. There is a vast array of further Quantum Field Theory texts, many of them with 1. Also because the Klein-Gordon equation is second order in time, it has the solutions with either sign of energy . It is the equation of motion of a quantum scalar or pseudoscalar field Klein-Gordon equation (1. The equation has attracted much at- DECAY ESTIMATES FOR THE KLEIN-GORDON EQUATION IN CURVED SPACETIME MUHAMMET YAZICI Abstract. Klein-Gordon equation with critical nonlinearity and inhomogeneous Dirichlet boundary conditions Naumkin, I. M. Time-fractional Klein-Gordon equation: formulation and solution using variational methods YOUWEI ZHANG Hexi University School of Mathematics and Statistics Klein-Gordon Fields : Positive definite only if restricted to (combinations of) positive frequency solutions of the Klein-Gordon equation In the thesis we will discuss some recent developments for a particular semi-linear defocusing wave equation: the semilinear ujujp 1 Klein-Gordon equation, focusing on the two and three space dimensions cases. The Klein-Gordon Equation. It is the equation of motion of a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. 3 is itself incapa Klein{Gordon Equation for the Quantum Fields Thus far in class have introduced the (free) quantum scalar eld ^’(x;t), its canonically conjugate quantum eld ^ˇ(x;t), their equal-time commutation relations The Klein–Gordon equation is encountered in quantum field theory and a number of applications. In the present paper, we couple double Laplace transform with Iterative method to solve nonlinear Klein-Gordon equation subject to initial and boundary conditions. 1 Lecture 31: Introduction to Klein-Gordon Equation Physics 452 Justin Peatross 31. Invariance of ψ under rotations means that, if valid at all, Klein-Gordon equation limited to spinless particles To find the Klein-Gordon equation for a spin zero particle interacting with an electro-magnetic field, replace ∂ µ by ∂ µ + iqA µ where qis the charge of the particle,A µ is the isthe four dimensional vectorpotential. June 2013 – 06. The idea of Dirac was to demand that there be Hamiltonian that is linear in such the square of would give the required formula 1 Nakao Hayashi, Pavel I. Strictly as per the compliance and regulations of : Klein-Gordon Equation for a Particle in Brane A new class of exact solutions of the bound Dirac and bound Klein Gordon equations in non co propagating plane waves is found. The Klein-Gordon equation and Antimatter Kevin Gibson May 18, 2011 Introduction Physicists employ different equations to solve for the quantum behavior of matter KLEIN-GORDON EQUATION IN SCHRÖDINGER FORM 3 which is the usual relativistic formula for the energy of a particle. org 2 | P a g e describes, for example, structural phase transitions in ferroelectric and ferromagnetic materials, topological Fourier uniqueness sets and the Klein-Gordon equation 3 We should understand the invariance properties of local Heisenberg uniqueness pairs with We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ. klein gordon equation