Описание спектра водородоподобного атома в квантовой механике с последователь но вероятностной интерпретацией

In the first part of the work, the authors review selected statistical interpretations of nonrelativistic quantum mechanics. Then they discuss a possible version of quantum mechanics admitting a nonnegative quantum distribution function. In this version, the time-independent Schr{ö}dinger equation for a particle in a potential field V(bold{r}) is left[-frac{hbar^{2}}{2m}Delta +introman{d}^{3}{bfrho}, alpha_{0}({bfrho}) V(bold{r}+{bfrho})right] Psi(bold{r})=EPsi(bold{r}), where alpha_{0}({bfrho})geq0. par In the second part of the work, the authors consider this modified Schr{ö}dinger equation in the Coulomb case, i.e., for V(bold{r})=-Ze^{2}/|bold{r}|. On applying Kato's perturbation theory for selfadjoint operators, some estimates for the discrete part of a spectrum of the modified Schr{ö}dinger eigenproblem are provided.