"Probability current" Psi = a(x,y,z,t) + i b(x,y,z,t) -- make Psi complex valued J = i hbar / (2 m) (Psi grad(conj(Psi)) - conj(Psi) grad(Psi)) L(f) = div(grad(f)) -- Laplacian "Verify equation (3)" check(div(J) == i hbar / (2 m) (Psi L(conj(Psi)) - conj(Psi) L(Psi))) "ok" -- Schrodinger equation dt(f) = i hbar / (2 m) div(grad(f)) - i / hbar V(x,y,z,t) f check(dt(conj(Psi)) == -conj(dt(Psi))) "Verify equation (6)" check(-div(J) == conj(Psi) dt(Psi) - Psi dt(conj(Psi))) check(-div(J) == conj(Psi) dt(Psi) + Psi conj(dt(Psi))) "ok" Run