Gaussian

The gaussian solution is spherically symmetric about the origin of the Cartesian coordinate system, and is time symmetric. The initial profile is

$$\phi(r) = A \exp (- r^2/\sigma)$$ (part1074)

with the solution at the origin being

$$\Psi(r=0,t) = \left(1-2\frac{t^2}{\sigma}\right)\exp(-t^2/\sigma)$$ (part1075)

The Gaussian solution is set with the parameters

• amplitude = $A$

• sigma = $\sigma$