THE UNCERTAINTY WAY OF GENERALIZATION OF COHERENT STATES

D.A. Trifonov
Institute for Nuclear Research, 72 Tzarigradsko chaussee, 1784 Sofia, Bulgaria
 
 

Abstract.
The three ways of generalization of canonical coherent states are briefly reviewed and
compared with the emphasis laid on the (minimum) uncertainty way. The characteristic
uncertainty relations, which include  the Schroedinger and Robertson inequalities, are extended
to the case of several states. It is shown that the standard SU(1,1) and SU(2) coherent states
are the unique states which minimize the second order characteristic inequality for the three
generators. A set of states which minimize the Schroedinger inequality for the Hermitian
components of the su_q(1,1) ladder operator is also constructed. It is noted that the
characteristic uncertainty relations can be written in the alternative complementary form.
 
 
 
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