Distance Formula for Grassmann Manifold --Applied to Anandan--Aharonov   Type Uncertainty Relation--
  The time-energy uncertainty relation of Anandan-Aharonov is generalized to a relation involving a set of quantum state vectors. This is achieved by obtaining an explicit formula for the distance between two finitely separated points in the Grassmann manifold. 
Minoru Hirayama, Takeshi Hamada and Jin Chen