GENERALIZED  INTELLIGENT  STATES  AND SQUEEZING

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

Abstract.
The Robertson-Schroedinger uncertainty relation for two observables A and B is shown
to be minimized in the eigenstates of the operator \lambda A + iB, \lambda being a complex
number. Such states, called generalized intelligent states (GIS), can exhibit arbitrarily strong
squeezing of A or B. The time evolution of GIS is stable for Hamiltonians which admit linear
in A and B invariants.
Systems of GIS for the  SU(1,1) and  SU(2) groups are constructed and discussed.  It is
shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and
Girardello CS  while the spin CS are a subset of  SU(2)  GIS. CS for an arbitrary semisimple
Lie group can be considered as GIS for the quadratures of the Weyl generators.
PACS' numbers 03.65.Ca; 03.65.Fd; 42.50.Dv.
 
 
 
  Back to Publications