A Bohmian total potential view to quantum effects. I. Methodology and simple model systems

The coherent-state wave packet dynamics of several model systems is analyzed in terms of Bohm's total potential. The quantum dynamics has been obtained by solving the time-dependent Schroedinger equation, and a method for obtaining the total potential from it, involving just matrix algebra, has been proposed. Contrary to what one may expect, it is shown that the time- and state-dependent features of the total potential admit a rationale, classical-like description of quantum effects, leading to a unified picture of them, which is not critically dependent, as for the key features, on the classical potential. An outstanding feature is found to be the relation of the state system's density amplitude and sharpness (in its dependence with position) with quantum effects. Sharp density profiles and low densities cause the total potential to strongly depart from the classical value, in both time regimes and position ranges, which provide a clearer, more deterministic view to quantum dynamics. Free motion as well as scattering processes by square and Eckart barriers have been analyzed by means of careful inspection of several time dependent snapshots. The result is an insightful picture of processes involving tunneling and antitunneling, including their dynamical variants, as well as resonances and quantization