Determining the quantum mechanical behavior of many interacting particles is essential to solving important problems in a variety of scientific fields, including physics, chemistry and mathematics. For instance, in order to describe the electronic structure of materials and molecules, researchers first need to find the ground, excited and thermal states of the Born-Oppenheimer Hamiltonian approximation. In quantum chemistry, the Born-Oppenheimer approximation is the assumption that electronic and nuclear motions in molecules can be separated.