Information entropies for eigendensities of homogeneous potentials

Abstract

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.