  In this article, we try to test the influence of the modification of the
scalar product, found in the problems of the energy-dependent potential, on the
physical properties of the harmonic oscillator in one dimension. For this, we
at first discuss the effect of this change on the thermodynamic properties of
this oscillator, and then on the parameter of Fisher, well known in the field
of quantum information. For the second problem, we are an obligation to
redefine this parameter. Finally, the uncertainly relation of Cramer-Rao is
well recovered in our problem in question.
