Interaction of a quantum particle with gravitational wave in modified gravity theory

We present the formal solution for a quantum mechanical particle responding to gravitational wave (GW) in the framework of modified theories of gravity (MTG) where, apart from the two standard tensorial modes of polarization of GW, we have considered an additional scalar mode. The presence of this longitudinal scalar mode makes it necessary to extend the usual two-dimensional description of matter-GW interaction to a three-dimensional one. Naturally this requires non-trivial changes in the quantum mechanical treatment which we elaborate in this paper.