Hilbert space vector space absolute squares
So that the infinite list of amplitudes 



(
…
,

ψ

−
2


,

ψ

−
1


,

ψ

0


,

ψ

1


,

ψ

2


,
…
)


{\textstyle (\ldots ,\psi _{-2},\psi _{-1},\psi _{0},\psi _{1},\psi _{2},\ldots )}

 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:
