  In this work we propose a new approach to the explanation of the nature of
electron based on the corpuscular-wave monism using the further development of
the optical-mechanical analogy to describe the physical reality. In this theory
the motion of an electron is considered to occur along a trajectory the
presence of which is a reflection of the existence of a particle, as well as it
is assumed that any motion is defined by a wave V(x,t). It is assumed that
there is an explicit relationship between the trajectory and wave equations of
the electron, which are established on the basis of the local variational
principle. In this approach, an electron wave propagating in free space takes
along the electron trajectory. We used this theory to describe the electron
motion in a hydrogen-like atom and found its stationary states. The energies of
these states coincide with the known quantum mechanics solutions for the
stationary energies of the hydrogen-like atom, however, in our approach the
spatial trajectories of the electron have the form of the surfaces, which are
formed in the region of nodes of the standing electron wave. These surfaces
have the form of spheres for the spherical symmetrical electron states and the
radii of these spheres coincide with the radii of the Bohr orbits of these
states. Thus, in this approach the trajectory and wave measurements of the
electron get a consistent spatial description that is inherent to the picture
of the corpuscular-wave monism. We discuss the considerable correspondence of
the proposed theory with the quantum mechanics results describing the
stationary and non-stationary motions of the electron in the atom and their
difference. We believe that measuring of the spatial configuration of the
observed electron trajectory surfaces in an atom could be a deep examination of
the standard quantum theory.
