## Intiutive approach to Green's function for SE

Griffiths develops an intelgral equation for Scrödinger equation in his QM book. As doing so, he requires Green's function for Helmholtz equation

$$(k^2 + \nabla^2) G( \mathbf r) = \delta^3(\mathbf r)$$

A rigourious series of steps, including Fourier transforms and residue integrals follow immidiately. As it turns out, the Green's function is independent of direction of $\mathbf r$, i.e. $G(\mathbf r) = G(r)$. Does anyone know a trick deducing this condition without actually finding the Green's function. The importance to prove is that, it turns out that there's a relatively simple solution if we assume $G(\mathbf r) = G(r)$)
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 Blog Entries: 9 Recognitions: Homework Help Science Advisor This simpler form of the GF is caused by a space-invariance of the potential.