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Relative Fisher information (IR), which is a measure of correlativefluctuation between two probability densities, has been pursued for a number ofquantum systems, such as, 1D quantum harmonic oscillator (QHO) and a fewcentral potentials namely, 3D isotropic QHO, hydrogen atom and pseudoharmonicpotential (PHP) in both position ($r$) and momentum ($p$) spaces. In the 1Dcase, the $n=0$ state is chosen as reference, whereas for a central potential,the respective circular or node-less (corresponding to lowest radial quantumnumber $n_{r}$) state of a given $l$ quantum number, is selected. Starting fromtheir exact wave functions, expressions of IR in both $r$ and $p$ spaces areobtained in closed analytical forms in all these systems. A careful analysisreveals that, for the 1D QHO, IR in both coordinate spaces increase linearlywith quantum number $n$. Likewise, for 3D QHO and PHP, it varies with singlepower of radial quantum number $n_{r}$ in both spaces. But, in H atom theydepend on both principal ($n$) and azimuthal ($l$) quantum numbers. However, ata fixed $l$, IR (in conjugate spaces) initially advance with rise of $n$ andthen falls off; also for a given $n$, it always decreases with $l$.

Relative Fisher information in some central potentials