We investigate the interaction of the gravitational field with a quantum particle. We derive the wave equation in the curved Galilean space-time 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 Schrödinger equation and without 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.

PACS numbers: 04.20.-q