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x)=u_{0}(x)\\in H^{2}({\\bf{R}}^{N}),\n  \\end{aligned}\\right.\n  \\end{equation*} If $N>8$, \\ $1+\\frac{8}{N}<p<1+\\frac{8}{N-4}$ (i.e. the $L^{2}$-supercritical and $\\dot{H}^{2}$-subcritical case ), and $\\langle x\\rangle^\\beta \\big(|V(x)|+|\\nabla V(x)|\\big)\\in L^\\infty$ for some $\\beta>N+4$, then we firstly prove a global well-posedness and scattering result 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