The use of a computer has become a necessity for the modeling of quantum systems. Advances in computational power and algorithms have allowed scientists to approximate the structures and properties of various molecules. Yet as the size of the quantum system grows, the computational time and space complexity grows exponentially. An alternative approach was proposed in a separate study by Dave Wecker which forgoes the expensive computational requirements for molecule simulations. Rather than calculating out the terms of the Hamiltonian in Schrodinger’s equation, artificial molecules were modeled by randomly sampling from probability distribution functions.
In this paper we explore the validity of this approach by testing our own calculated energies of the hydrogen molecule against the randomly sampled Wecker ensemble. We find that overall the distributions generated randomly range from being largely off from reality to being of a similar enough distribution that the study invites further investigation. This suggests there may be value in random sampling so long as we choose the appropriate probability distribution with the correct parameters.