As an example, consider a quantum mechanical particle in one spatial dimension, in the configuration space representation. Here the Hilbert space is H = L 2 ( R ) , the space of square-integrable functions on the real line. Vectors ψ ψ ∈ ∈ H are represented by functions ψ ψ ( x ) , called wave functions. The scalar product is given by ⟨ ⟨ ψ ψ 1 | ψ ψ 2 ⟩ ⟩ = ∫ ∫ ψ ψ 1 ∗ ∗ ( x ) ψ ψ 2 ( x ) d x . The wave functions have a direct interpretation as a probability distribution: