Schroedinger uncertainty relation and its minimization states

Details Schroedinger uncertainty relation and its minimization states Schroedinger uncertainty relation and its minimization states

2001-05-12

arxiv.org/abs/physics/0105035v1

Phys.World 24 (2001) 107-116

Physics

Atomic Physics

Latex, 10 pages, 3 figures. Introductory review (on the occasion of the 70th anniversary of Schroedinger original paper)

Scientific paper

An introductory survey on the Schroedinger uncertainty relation and its minimization states is presented with minimal number of formulas and some historical points. The case of the two canonical observables, position and momentum, is discussed in greater detail: basic properties of the two subsets of minimization states (canonical squeezed and coherent states) are reviewed and compared. The case of two non-canonical observables is breafly outlined. Stanfard SU(1,1) and SU(2) group-related coherent states can be defined as states that minimize Schroedinger inequality for the three pairs of generators simultaneously. The symmetry of the Heisenberg and Schroedinger relations is also discussed, and two natural generalizations to the cases of several observables and several states are noted.

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