Mechanics and thermodynamics of the "Bernoulli" oscillators (uni-dimensional closed motions) Part II : Solved examples and classical limit

In the previous Part I of this paper, we developed a theoretical model to account for energy and mass fluctuations in oscillators dynamics, thus providing a peculiar but classical-like insight into the quantum mechanical behaviour. The model helps with a variable density-current assumption, supported by a mass effect finding in turn its expression in what we call ''the mass eigenfunctions''. In the present Part II of the paper, we have worked out numerical solutions for the two basic examples of the harmonic oscillator and the (infinetely deep) rectangular well. Calculations are strongly non-linear and submitted to strict integral and differential constraints, so that we have to perform them in two steps. First the unknown function gn(x), entering the mass function expression, is taken equal to 1. This gives solutions leaving the phase quantization condition affected by a (small) error. In a second step, a numerical correction is imposed to the previous solutions in such a way that the phase errors are suppressed. So we believe having provided here detailed proof of consistency between the variable-current wave equation and the classical energy theorem (inclusive of a peculiar expression of the quantum potential inside it), whose forms we gave theoretically in the previous Part I of this work. Graphs and tables are here shown and discussed extensively for a sampled set of quantum levels of both the chosen cases. They are exhaustive, in that we can draw out from them a general insight into the classical limit. This last reveals very peculiar to our model in comparison with the JWKB standard framework.