  Relative Fisher information (IR), which is a measure of correlative
fluctuation between two probability densities, has been pursued for a number of
quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few
central potentials namely, 3D isotropic QHO, hydrogen atom and pseudoharmonic
potential (PHP) in both position ($r$) and momentum ($p$) spaces. In the 1D
case, the $n=0$ state is chosen as reference, whereas for a central potential,
the respective circular or node-less (corresponding to lowest radial quantum
number $n_{r}$) state of a given $l$ quantum number, is selected. Starting from
their exact wave functions, expressions of IR in both $r$ and $p$ spaces are
obtained in closed analytical forms in all these systems. A careful analysis
reveals that, for the 1D QHO, IR in both coordinate spaces increase linearly
with quantum number $n$. Likewise, for 3D QHO and PHP, it varies with single
power of radial quantum number $n_{r}$ in both spaces. But, in H atom they
depend on both principal ($n$) and azimuthal ($l$) quantum numbers. However, at
a fixed $l$, IR (in conjugate spaces) initially advance with rise of $n$ and
then falls off; also for a given $n$, it always decreases with $l$.
