Welcome to the presentation of Viggo Kanljung's and Wilhelm Öhlin's Bachelor's thesis presentation with the title "A study of the Green's function for the Klein-Gordon equation".

Abstract: This paper explores the Klein-Gordon equation, a relativistic wave equation. More specifically, it studies the free form of the equation, where the potential is set to zero. The partial differential equation, together with initial conditions, forms an initial value problem. The first goal of the paper is to derive Green’s function for the problem. This is done in several ways, using spectral theory, double transforms, and a domain mapping approach. The Green’s function is then validated, checking that it fulfills the differential equation and the initial condition. The authors then turn to asymptotic analysis, deriving a formula for the asymptotic behavior of the resulting Bessel function. Lastly, the asymptotic characteristics are confirmed using numerical analysis.

Handledare: Sara Maad Sasane
Examinator: Wilhelm Treschow