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

Trajectory-Wave Approach to Electron Dynamics in Hydrogen Atom