  It is a matter of fact that the universe lives on a Gravitational Wave
Background (GWB). This GWB is extra energy that is not contained in Einstein's
equations. In \cite{Matos:2021jef}, a new model was developed to explain the
accelerating expansion of the universe where a GWB was incorporated into
Einstein's equations by extending them as
$R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}+\frac{2\pi^2}{{\lambda}^2}g_{\mu\nu}=\kappa
^2 T_{\mu\nu}$, where ${\lambda}$ is the Compton wavelength of the graviton. In
this paper, we continue to study this new paradigm. Due to GWB, quantum
particles cannot follow geodesics, but rather stochastic trajectories. In the
present work, we start by adding a stochastic term to the trajectories of
quantum particles and derive the corresponding field equations of a quantum
particle. We arrive at the Klein-Gordon equation in curved spacetime and from
it we obtain a generalized Schr\"odinger equation. This leads to the following
relevant result: the Schr\"odinger equation can be a direct consequence of the
fact that the universe lives on a GWB.
