We calculate the information entropy of single-particle states in
position-space Srβ and momentum-space Skβ for a nucleon in a nucleus, a
Ξ particle in a hypernucleus and an electron in an atomic cluster. It
is seen that Srβ and Skβ obey the same approximate functional form as
functions of the number of particles, Srβ ({\rm or} Skβ)=a+bN1/3
in all of the above many-body systems in position- and momentum- space
separately. The net information content Srβ+Skβ is a slowly varying
function of N of the same form as above. The entropy sum Srβ+Skβ is
invariant to uniform scaling of coordinates and a characteristic of the
single-particle states of a specific system. The order of single-particle
states according to Srβ+Skβ is the same as their classification according to
energy keeping the quantum number n constant. The spin-orbit splitting is
reproduced correctly. It is also seen that Srβ+Skβ enhances with
excitation of a fermion in a quantum-mechanical system. Finally, we establish a
relationship of Srβ+Skβ with the energy of the corresponding single-particle
state i.e. Srβ+Skβ=kln(ΞΌE+Ξ½). This relation holds for all the
systems under consideration.Comment: 9 pages, latex, 6 figure