  In this paper, we consider the following three dimensional defocusing cubic
nonlinear Schr\"odinger equation (NLS) with partial harmonic potential
  \begin{equation*}\tag{NLS}
  i\partial_t u + \left(\Delta_{\mathbb{R}^3 }-x^2 \right) u = |u|^2 u, \quad
u|_{t=0} = u_0.
  \end{equation*}
  Our main result shows that the solution $u$ scatters for any given initial
data $u_0$ with finite mass and energy.
  The main new ingredient in our approach is to approximate (NLS) in the
large-scale case by a relevant dispersive continuous resonant (DCR) system. The
proof of global well-posedness and scattering of the new (DCR) system is
greatly inspired by the fundamental works of Dodson \cite{D3,D1,D2} in his
study of scattering for the mass-critical nonlinear Schr\"odinger equation. The
analysis of (DCR) system allows us to utilize the additional regularity of the
smooth nonlinear profile so that the celebrated
concentration-compactness/rigidity argument of Kenig and Merle applies.
