  Electromagnetic phenomena can be described by Maxwell equations written for
the vectors of electric and magnetic field. Equivalently, electrodynamics can
be reformulated in terms of an electromagnetic vector potential. We demonstrate
that the Schr\"odinger equation admits an analogous treatment. We present a
Lagrangian theory of a real scalar field $\phi$ whose equation of motion turns
out to be equivalent to the Schr\"odinger equation with time independent
potential. After introduction the field into the formalism, its mathematical
structure becomes analogous to those of electrodynamics. The field $\phi$ is in
the same relation to the real and imaginary part of a wave function as the
vector potential is in respect to electric and magnetic fields. Preservation of
quantum-mechanics probability is just an energy conservation law of the field
$\phi$.
