Show that the free-particle schrodinger equation is equivalent to two real equations involving two real functions ψ₁(x, t) and ψ₂(x, t), as follows:
h²/2m ∂²ψ₁(x, t)/∂²x = h ∂ψ₂(x, t)/∂t

-h²/2m ∂²ψ₂(x, t)/∂²x = h ∂ψ₁(x, t)/∂t