Sommerfeld Radiation Condition
This is a condition for the Frequency Domain Problem that the scattered wave is only outgoing at infinity. It depends on the convention regarding whether the time dependence is or . Assuming the former (which is the standard convention on this wiki). In two dimensions the condition is
where is the incident potential and is the wave number.
In three dimensions the condition is
If the time dependence is assumed to be , then we have in two dimensions
and in three dimensions