MC simulation the solution of the Schro¨dinger equation for an N-electron system,

MC Simulations versus MC calculations One can distinguish between two kinds of algorithms: 1. The system being studied is stochastic and the stochasticity of the algorithm mimics the stochasticity of the actual system. e.g. study of neutron transport and decay in nuclear reactor by following the trajectories of a large number of neutrons. Such problems are suitable for MC algorithms in a very obvious way. 2. Much more interesting are applications where the system being studied is not stochastic, but nevertheless a stochastic algorithm is the most efficient, or the most accurate, or the only feasible method for studying the system. e.g. the solution of a PDE in a large number of variables, e.g., the solution of the Schro¨dinger equation for an N-electron system, with say N = 100 or 1000. (Note: The fact that the wavefunction has a probabilistic interpretation has nothing to do with the stochasticity of the algorithm. The wavefunction itself is perfectly deterministic.)