  We consider the question of Quantum Unique Ergodicity for quasimodes on
surfaces of constant negative curvature, and conjecture the order of quasimodes
that should satisfy QUE. We then show that this conjecture holds for Eisenstein
series on the modular surface, extending results of Luo-Sarnak and Jakobson.
Moreover, we observe that the equidistribution results of Luo-Sarnak and
Jakobson extend to quasimodes of much weaker order--- for which QUE is known to
fail on compact surfaces--- though in this scenario the total mass of the limit
measures will decrease. We interpret this stronger equidistribution property in
the context of arithmetic QUE, in light of recent joint work with E.
Lindenstrauss on joint quasimodes.
