  Consider the global wellposedness problem for nonlinear
  Schr\"odinger equation \[ i\partial_t u = [-\tfrac{1}{2} \Delta + V(x)] u \pm
|u|^{4/(d-2)} u, \ u(0) \in \Sigma(\mathbf{R}^d), \] where $\Sigma$ is the
weighted Sobolev space $\dot{H}^1 \cap |x|^{-1} L^2$. The case $V(x) =
\tfrac{1}{2}|x|^2$ was recently treated by the author. This note generalizes
the results to a class of "approximately quadratic" potentials.
  We closely follow the previous concentration compactness arguments for the
harmonic oscillator. A key technical difference is that in the absence of a
concrete formula for the linear propagator, we apply more general tools from
microlocal analysis, including a Fourier integral parametrix of Fujiwara.
