  W. Luo and P. Sarnak have proved the quantum unique ergodicity property for
Eisenstein series on $\rm{PSL}(2,\mathbb{Z}) \backslash H$. We extend their
result to Eisenstein series on $\rm{PSL}(2,O) \backslash H^n$, where $O$ is the
ring of integers in a totally real field of degree $n$ over $Q$ with narrow
class number one, using the Eisenstein series considered by I. Efrat. We also
give an expository treatment of the theory of Hecke operators on
non-holomorphic Hilbert modular forms.
