Cancellation of two heat-kernel impulses
= Cancellation of two heat-kernel impulses
On the real line, initial data $\delta(x-2\sqrt D)$ and a source $-A\delta(x+2\sqrt D)\delta(t-1)$ produce
$$
K_t(x-2\sqrt D)-AH(t-1)K_{t-1}(x+2\sqrt D).
$$
At $x=0,t=2$, the two terms cancel exactly for $A=\sqrt{e/2}$.