In other terms, if – at a certain instant of time – the particle is in the state represented by a square integrable wave function ψ ψ and assuming the wave function ψ ψ be of L 2 -norm equal 1, ‖ ‖ ψ ψ ‖ ‖ 2 = ∫ ∫ − − ∞ ∞ + ∞ ∞ | ψ ψ | 2 d x = 1 , then the probability to find the particle in the position range [ a , b ] is π π X ( ψ ψ ) ( [ a , b ] ) = ∫ ∫ a b | ψ ψ | 2 d x .