So that the infinite list of amplitudes ( … … , ψ ψ − − 2 , ψ ψ − − 1 , ψ ψ 0 , ψ ψ 1 , ψ ψ 2 , … … ) completely describes the quantum state of the particle. This list is called the state vector, and formally it is an element of a Hilbert space, an infinite-dimensional complex vector space. It is usual to represent the state so that the sum of the absolute squares of the amplitudes is one: