# High dimensional wave equation

In 3 dimensions, the wave equation $$\Box\psi=\delta(t)\delta(\vec{x})$$ has the retarded and advanced solutions $$\psi=A_R \frac{\delta(t-x)}{4\pi x} + A_A \frac{\delta(t+x)}{4\pi x}.$$ How does this generalize to higher dimensions?

• Are you asking what the differential equation is in higher dimensions? Or what the solutions are? – G. Smith Feb 28 at 16:48
• Surely you can adapt this. – Cosmas Zachos Feb 28 at 17:02
• ... or this. – Cosmas Zachos Feb 28 at 17:08
• ...or THIS one. Can you fold it into your question? – Cosmas Zachos Feb 28 at 17:50
• Umm, I'm not sure how to do "fold" it into my question. But let me check the link, if it's good then I guess the problem is resolved. – K. Sadri Feb 28 at 18:32

The idea is to express the N-dimensional Laplacian in polar coordinates, $$\frac{1}{r^{N-1}} \frac{\partial}{\partial r} \left(r^{N-1} \frac{\partial }{\partial r} \right)$$.