  Let X be a symplectic manifold and Aut(L) the automorphism group of a
Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M.
Souriau in the 1990s, are certain positive-definite functions on Aut(L) or,
less ambitiously, on any "large enough" subgroup G of Aut(L). This definition
has two major drawbacks: when G=Aut(L) there are no known examples; and when G
is a Lie subgroup the notion is, as we shall see, far from selective enough. In
this paper we introduce the concept of a quantum state *localized at Y*, where
Y is a coadjoint orbit of a subgroup H of G. We show that such states exist,
and tend to be unique when Y has lagrangian preimage in X. This solves, in a
number of cases, A. Weinstein's "fundamental quantization problem" of attaching
state vectors to lagrangian submanifolds.
