Transmutation operators for an angular Schrodinger type equation

Ponente(s): Jorge Sigfrido Macias Medina

In this work, we study the time-independent homogeneous Schrödinger equation in a bounded domain. We assume the potential "q" is a continuously differentiable function that depends on the angular component. A transmutation operator sending harmonic functions into solutions of that equation is constructed by determining its kernel "H" along with the PDE it satisfies and its initial conditions. The existence of such kernel is proven by applying Picard's theorem. Lastly, we prove the boundedness and invertibility of our operator and construct a complete family of solutions for this Schrödinger equation.