Аннотация

Stability condition of hypercomplex algebras under primitive mapping of 2D fractal spaces yields formulation of Schrodinger equation and endows its solutions (wave functions) and respective 3D objects with specific geometric images. In particular it is shown that the simplest 1D-box solution comprising no parameters of a particle’s motion can be interpreted as a 2D inhomogeneous string oscillating on real-imaginary fractal surface or as a 3D static spindle with harmonically distributed mass specter. Description of an inertially moving similar object is obtained with use of Bargmann-type theorem applied to Bohm equations, and as an exact solution of the equations, the fractal function containing explicit kinematic terms.

Keywords: Schrodinger equation, Bohm equations, 1D-box solution, quantum geometric models