In non-relativistic quantum mechanics, the probability current j of the wave function Ψ of a particle of mass m in one dimension is defined as j = ℏ ℏ 2 m i ( Ψ Ψ ∗ ∗ ∂ ∂ Ψ Ψ ∂ ∂ x − − Ψ Ψ ∂ ∂ Ψ Ψ ∗ ∗ ∂ ∂ x ) = ℏ ℏ m ℜ ℜ { Ψ Ψ ∗ ∗ 1 i ∂ ∂ Ψ Ψ ∂ ∂ x } = ℏ ℏ m ℑ ℑ { Ψ Ψ ∗ ∗ ∂ ∂ Ψ Ψ ∂ ∂ x } , where