An alternative quantization procedure for the Hydrogen atom

We introduce a (non-standard) laplacian form producing squared angular momentum values equal to ћ2[ l(l+1)+1/4]. So we set up an ”alternative” Hydrogen atom model, which can also be thought as a sort of precursor to the standard quantum atom. It shows the following properties : torus-like orbitals ; appearance of a ”zero point” rotational quantum number (it adds zenithal altitude fluctuations with momentum ћ/2); S-like wavefunctions made zero over nucleus; corrections to spectroscopic terms, linearly dependent on the operators ˆlz and ˆl^2ns, identical to the standard ones ; quantization procedure resolvable into a quantization in the constant azimuth plane, followed by rotation around the polar axis. Although we come to a subtlety concerning the azimuthal component, these features make the model suitable for decomposition in one-dimensional motions, whose quantum properties we could recently approach by a method based on ergodic statistics of classical-like time laws with variable mass. Comparing the present results with the standard quantum theory and the corresponding quasi-classical case, we trace a possible path to implement our one-dimensional calculations up to describe 2D and 3D motions; and to identify some ultimate differences, worth of further investigation, with those standard models.