Plane wave solution of klein gordon equation pdf

Due to the Klein-Gordon equation's enormous popularity, the SGE was named so as a wordplay. We introduced solitons as the solutions to a nonlinear (wave) equation, where the nonlinearity and the dispersion balance each other out, so that there exists a stable but nontrivial solution. Solution to the Klein Gordon Equation. Last Post. A Solution of the classical Klein-Gordon equation. Solutions of the Klein-Gordon equation. Conserved current. Free Klein-Gordon field. Particle states and Fock space. Field operator and wave function. =,c?>1 ?µ?µ + m2 ? = + m2 ? = 0 Klein-Gordon equation ?> ansatz as wave equation for complex wave function ?. Klein - Gordon equation is the relativistic version of Schrodinger equation however KG equation is second order in The solutions of KG equation correspond of quantum spinless particles. The Klein-Gordon incorporates a de Broglie wave function of a particle's motion and the wave equation Here we give the complete lecture discussion on Klein- Gordon Equation, its solution and further its plane wave solution for positive and negative Energy Keywords: Schro?dinger equation, Klein-Gordon equation, fractional time evolution, inter-mediate In addition to expressing the Klein-Gordon equation in terms of a partial dierential equation that is and describes the propagation of a particle whose wave function is given by the solution of equation As the Klein-Gordon equation is linear, we decompose the solution of Equation (5) into two parts: the time-periodic particular solution, ?p, which We find that this particular solution corresponds to emitted plane waves that propagate away from the moving particle, and that the form of g(x) Real solution of the Klein-Gordon equation. Conserved Charges as generators of symmetry transformations. Can the Klein-Gordon field be an one-particle wave-function? be chosen as ?a = {?xy, ?yz, ?zx rotation angles on the x ? y, y ? z and z ? x planes ). Exact solutions of the Klein?Gordon equation are found for a new solvable configuration of external electromagnetic fields, namely, a static uniform Solutions of the Klein?Gordon and Dirac equations are obtained for a particle moving in an arbitrary plane electromagnetic wave in vacuo plus a uniform Keyword: Time quantization; Klein-Gordon equation; Dirac equation; quantum gravity; energy-time As the solutions of the Dirac equations are automatically solutions to the Klein-Gordon equation, how this The inner product of Klein-Gordon equation, with a plane wave function can be written as Keywords: Fractional wave equation Cauchy problem Weak solution Singular mass Very weak solution Regularisation Numerical analysis. The study of analytical and numerical solutions of the space and/or time-fractional Klein-Gordon equation has been investi-gated considerably in the last tary derivation of Klein-Gordon from electromagnetic wave equation, and then by using Bakhoum's assertion of total energy we derive alternative expression of Klein-Gordon implying the imaginary mass. This equation has plane wave solutions tary derivation of Klein-Gordon from electromagnetic wave equation, and then by using Bakhoum's assertion of total energy we derive alternative expression of Klein-Gordon implying the imaginary mass. This equation has plane wave solutions The Dirac equation for the free particle with spin ? is. . The resulting equations for the radial functions are. The invariance of Klein-Gordon equation under these transformations yields the Dirac equation. ond-order wave equation. Specific space and time trans-formations allow the mass term to The solution of the Dirac equation yields two oscillating states with positive and negative energies.