em] of a

hydrogenlike system are well known: considering the ground energy state with n = 1 only, they are [[epsilon].

QUINTERO, On recurrence relations for radial wave functions for the N-th dimensional oscillators and hydrogenlike atoms: analytical and numerical study, Electron.

ALVAREZ-NODARSE, Recurrence relations for radial wave functions for the N-th dimensional oscillators and hydrogenlike atoms, J.

Besides, it is known that the hydrogenlike atom can be studied as a Morse oscillator, then here we prove that these fact leads to an interesting method to calculate <n[l.

Lee [6] showed that the Langer transformation [7] permits to study a non-relativistic hydrogenlike system as a vibrational Morse oscillator (MO), such that n gives the parameters of the Morse well and l determines an energy level in these well.

More than 40 years ago, experimenters succeeded in coaxing electrons and positrons into a short-lived coexistence as positronium, a

hydrogenlike atom with a positron replacing the proton.

The same holds for the energy levels of

hydrogenlike atoms.

2055-2068] we obtain some new recurrence relations for the radial wave functions of the N-th dimensional isotropic harmonic oscillators as well as the

hydrogenlike atoms.

Consisting of just one electron bound to a highly charged, heavy nucleus, such a

hydrogenlike ion serves as a testing ground for theories of atomic structure.

These ideas have been extended and checked in the papers [5,6] also for more complex quantum systems like

hydrogenlike and many electron atoms/ions and diatomic molecules; also these papers allowed concluding that eqs (1,1) efficiently replace the standard approach of wave mechanics, without requiring the concept of probability density and thus without need of calculating marginal distributions in the phase space through the Wigner functions.

The following example of calculation concerns first the nonrelativistic

hydrogenlike atom/ion.

3,1 is enough to calculate the energy levels of

hydrogenlike and many electron atoms/ions and diatomic molecules without solving any wave equation; then is attracting the idea that even the diffusion model can be formulated in terms of particles randomly spreading within their own delocalization space ranges conceptually arbitrary, unknown and unknowable themselves.