Consider the Helmholtz equation
$$(\Delta + 1) p(x) = 0 \quad \quad x \in \mathbb{R}^2$$
with the Sommerfield radiation condition applying to $p$. That is,
$$\lim_{|x| \to \infty} \bigg(\frac{\partial}{\partial |x|} - i \bigg) p(x) = 0.$$
Is a straightforward closed form analytic solution possible for this problem?