Hierarchy of local minimum solutions of Heisenberg's uncertainty principle

We derive a new hierarchy of local minimum Heisenberg-uncertainty states by introducing a superposition of "small waves" onto some initial state. Our objective is to increase the resolution in one observable, with the least decrease in the resolution in the conjugate observable. This leads to a constrained minimization which in a well-defined sense yields the best possible way of achieving this goal. The results are relevant to many topics (e.g., quantum optics and control, Bose-Einstein condensation, path integration, etc.).