  Ordinary intelligent states (OIS) hold equality in the Heisenberg uncertainty
relation involving two noncommuting observables {A, B}, whereas generalized
intelligent states (GIS) do so in the more generalized uncertainty relation,
the Schrodinger-Robertson inequality. In general, OISs form a subset of GISs.
However, if there exists a unitary evolution U that transforms the operators
{A, B} to a new pair of operators in a rotation form, it is shown that an
arbitrary GIS can be generated by applying the rotation operator U to a certain
OIS. In this sense, the set of OISs is unitarily equivalent to the set of GISs.
It is the case, for example, with the su(2) and the su(1,1) algebra that have
been extensively studied particularly in quantum optics. When these algebras
are represented by two bosonic operators (nondegenerate case), or by a single
bosonic operator (degenerate case), the rotation, or pseudo-rotation, operator
U corresponds to phase shift, beam splitting, or parametric amplification,
depending on two observables {A, B}.
