The derivation in three dimensions is the same, except the gradient operator del is used instead of one partial derivative. In three dimensions, the plane wave solution to Schrödinger's equation is: ψ ψ = e i ℏ ℏ ( p ⋅ ⋅ r − − E t ) and the gradient is ∇ ∇ ψ ψ = e x ∂ ∂ ψ ψ ∂ ∂ x + e y ∂ ∂ ψ ψ ∂ ∂ y + e z ∂ ∂ ψ ψ ∂ ∂ z = i ℏ ℏ ( p x e x + p y e y + p z e z ) ψ ψ = i ℏ ℏ p ψ ψ where e x, e y, and e z are the unit vectors for the three spatial dimensions, hence p ^ ^ = − − i ℏ ℏ ∇ ∇