Theoretical information measurement in nonrelativistic time-dependent approach

Abstract

The information-theoretic measures of time-dependent Schrodinger equation are investigated via the Shannon information entropy, variance and local Fisher quantities. In our calculations, we consider the two first states $$n = 0,1$$ and obtain the position $$S_{x} (t)$$ and momentum $$S_{p} (t)$$ Shannon entropies as well as Fisher information $$I_{x} (t)$$ in position and momentum $$I_{p} (t)$$ spaces. Using the Fourier transformed wave function, we obtain the results in momentum space. Some interesting features of the information entropy densities $$\rho_{s} (x,t)$$ and $$\gamma_{s} (p,t)$$ , as well as the probability densities $$\rho (x,t)$$ and $$\gamma (p,t)$$ for time-dependent states are demonstrated. We establish a general relation between variance and Fisher’s information. The Bialynicki-Birula–Mycielski inequality is tested and verified for the states $$n = 0,1$$ .