If we were to vary over all possible states with norm 1 trying to minimize the expectation value of H , the lowest value would be E 0 and the corresponding state would be the ground state, as well as an eigenstate of H . Varying over the entire Hilbert space is usually too complicated for physical calculations, and a subspace of the entire Hilbert space is chosen, parametrized by some (real) differentiable parameters α i (i = 1, 2,..., N). The choice of the subspace is called the ansatz. Some choices of ansatzes lead to better approximations than others, therefore the choice of ansatz is important.