  A new SU(1, 1) position-dependent effective mass coherent states (PDEM CS)
related to the shifted harmonic oscillator (SHO) are deduced. This is
accomplished by applying a similarity transformation to the generally deformed
oscillator algebra (GDOA) generators for PDEM system and construct a new set of
operators which close the su(1, 1) Lie algebra, being the PDEM CS of the basis
for its unitary irreducible representation. The residual potential is
associated to the SHO. From the Lie algebra generators, we evaluate the
uncertainty relationship for a position and momentum-like operators in the PDEM
CS and show that it is minimized in the sense of Barut-Girardello CS. We prove
that the deduced PDEM CS preserve the same analytical form than those of
Glauber states. We show that the probability density of dynamical evolution in
the PDEM CS oscillates back and forth as time goes by and behaves as classical
wave packet.
