Exact and approximate solutions to the Helmholtz, Schrödinger and wave equation in ${\mathbf{R}}^3$ with radial data

Adrian Kirkeby

We derive simple-to-evaluate, closed-form solutions to the inhomogeneous Helmholtz equation, $\Delta u+k^{2}u={\chi }_{B_{x_0,r}}$, the Schrödinger equation, $i\hbar \partial_t u + \frac{\…