  In this paper we calculate the position and momentum space information
entropies for the quantum states associated with a particular physical system,
i.e. the isotonic oscillator Hamiltonian. We present our results for its ground
states, as well as for its excited states. We observe that the lower bound of
the sum of the position and momentum entropies expressed by the Beckner,
Bialynicki-Birula and Mycielski (BBM) inequality is satisfied. Moreover, there
exist eigenstates that exhibit squeezing in the position information entropy.
In fact, entropy squeezing, which occurs in position, will be compensated for
by an increase in momentum entropy, such that the BBM inequality is guaranteed.
To complete our study we investigate the amplitude squeezing in $x$ and
$p$-quadratures corresponding to the eigenstates of the isotonic oscillator and
show that amplitude squeezing, again in $x$, will be revealed as expected,
while the Heisenberg uncertainty relationship is also satisfied. Finally, our
numerical calculations of the entropy densities will be presented graphically.
