In particular, this means that a system of N interacting particles in 3 dimensions is described by one vector whose components in a basis where all the X are diagonal is a mathematical function of 3 N -dimensional space describing all their possible positions, effectively a much bigger collection of values than the mere collection of N three-dimensional wavefunctions in one physical space. Schrödinger came to the same conclusion independently, and eventually proved the equivalence of his own formalism to Heisenberg's.