Completeness and geometry of Schrödinger minimum uncertainty states

The symmetry, geometry, and completeness properties of Schrödinger minimum uncertainty states (SMUS) are considered. SMUS are equivalent to the coherent states with maximal symmetry related to the semidirect product G=H w ×)SU(1,1), H w being the Heizenberg–Weyl group. The invariant measures on G and on the homogeneous space G/K are constructed as well as noninvariant resolution unity measures. The fiber bundle and the symplectic Kaehler structures of SMUS are elucidated with the implications to their stable evolution.