Soutions to the Midtermproblemset MIDTERM The potential of an atom where we have a pointlike proton in the middle and an electroncloud around it, which falls off exponentially is described by the formula:

exp(-ar)/r * (1 + r/2)

the first part (the "1"-part) stems from the proton and the other part is due to the electrondistribution. the potential has the following shape:

accordingly to the laplacian-equation we get the charge ditribution by :

laplacian (phi) = 4 pi rho

we also can plot this function, what gives us the following plot:

or if we only make a plot of the elecrondistribution alone, we get the following diagram: