  Shannon entropy and Fisher information functionals are known to quantify
certain information-theoretic properties of continuous probability
distributions of various origins. We carry out a systematic study of these
functionals, while assuming that the pertinent probability density has a
quantum mechanical appearance $\rho \doteq |\psi |^2$, with $\psi \in L^2(R)$.
Their behavior in time, due to the quantum Schr\"{o}dinger picture
evolution-induced dynamics of $\rho (x,t)$ is investigated as well, with an
emphasis on thermodynamical features of quantum motion.
