With special attention to the role of information theory in physical sciences we present analytical
results for the coordinate- and momentum-space Fisher information of some important one-dimensional
quantum systems which differ in spacing of their energy levels. The studies envisaged allow us to
relate the coordinate-space information ( ##IMG##
[http://ej.iop.org/images/0143-0807/38/2/025103/ejpaa51a0ieqn1.gif] {${I}_{\rho }$} ) with the
familiar energy levels of the quantum system. The corresponding momentum-space information ( ##IMG##
[http://ej.iop.org/images/0143-0807/38/2/025103/ejpaa51a0ieqn2.gif] {${I}_{\gamma }$} ) does not
obey such a simple relationship with the energy spectrum. Our results for the product ( ##IMG##
[http://ej.iop.org/images/0143-0807/38/2/025103/ejpaa51a0ieqn3.gif] {${I}_{\rho }{I}_{\gamma }$} )
depend quadratically on the principal quantum number n and satisfy an appropriate uncertai…