The problem on stationary states in self gravitational field

To follow is the problem on stationary states of an electron in its own gravitational field where the boundary conditions earlier described by S. I. Fisenko in 2015 J. Phys.: Conf. Ser. 574 012157 doi:10.1088/1742-6596/574/1/012157 are made specific. The simplest approximation provides an assessment of the energy spectrum of stationary states only. Nevertheless, this is enough to confirm the existence of such stationary states and to further elaborate a detailed solution of the problem on stationary states including determination of all the quantum numbers' spectra and corresponding wave functions. No other matters are discussed here. The case in hand is a purely mathematical problem, further physical interpretation of which is of a fundamental value.