Information entropies for eigendensities of homogeneous potentials

For homogeneous potentials, the sum S-T, of position and momentum Shannon information entropies S-r and S-p is shown to be independent of the coupling strength scaling. The other commonly used uncertainty like products also follow similar behavior. The ramifications of this scaling property in the cases of hydrogenlike, harmonic oscillator, Morse, and Poeschl-Teller potentials are discussed with the example of S-T. (c) 2006 American Institute of Physics.