User:Tomerma/drafts/uniq

Uniqueness of Potential
[FIXME] explain that for potential with known charge density and boundary conditions, the potential function is completely determined (i.e. no two different potential functions fulfill the requirements).

Proof
Explain that if there were two such functions we would look at the difference, it having a laplacian of zero and potential of zero on boundaries. Because of this the potential is zero everywhere.

Intuition
[FIXME] Explain in the 1D case that when the laplacian is zero that means the potential must be a line. That means that the minimum and maximum are achieved on the boundaries which are two points. So if they are determined, we have the original function.