Relaxation: from Laplace's equation to the heat equation and discretely back again

We see how the relaxation method for Laplace's equation is related to a numerical solution of the heat equation, which is in turn motivated by thinking of the Hamiltonian as the the time evolution operator in quantum mechanics. This gives some physical insight into what the relaxation method is doing. We also use this to suggest investigative work for a student learning about computational methods in physics. (paper)