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

Quantum Unique Ergodicity for Eisenstein Series on the Hilbert Modular Group over a Totally Real Field