  We study the quantum limits of Eisenstein series off the critical line for
$\mathrm{PSL}_{2}(\mathcal{O}_{K})\backslash\mathbb{H}^{3}$, where $K$ is an
imaginary quadratic field of class number one. This generalises the results of
Petridis, Raulf and Risager on
$\mathrm{PSL}_{2}(\mathbb{Z})\backslash\mathbb{H}^{2}$. We observe that the
measures $\lvert E(p,\sigma_{t}+it)\rvert^{2}d\mu(p)$ become equidistributed
only if $\sigma_{t}\rightarrow 1$ as $t\rightarrow\infty$. We use these
computations to study measures defined in terms of the scattering states, which
are shown to converge to the absolutely continuous measure $E(p,3)d\mu(p)$
under the GRH.
