  We investigate the interaction of the gravitational field with a quantum
particle. We derive the wave equation in the curved galilean spacetime from the
very broad Quantum mechanical assumptions and from covariance under the Milne
group. The inertial and gravitational masses are equal in that equation. So, we
give the proof of the equality for the non-relativistic quantum particle,
without applying the equivalence principle to the Schr\"odinger equation and
witout imposing any relation to the classical equations of motion. This result
constitutes a substantial strengthening of the previous result obtained by
Herdegen and the author.
