  With purely classical tools a model for a bouncer-walker system of an
elementary particle will be derived in this work which reflects the old idea of
de Broglie's particle-wave duality. This model contains, on the one hand, a
possible explanation of the work-energy exchange between the two separated
motions, thereby providing an energy quantisation as originally postulated by
Max Planck. On the other hand, the system perfectly obeys the Bohmian-type law
of motion in full accordance with quantum mechanics.
  For the calculation of elementary particles' trajectories a ballistic
diffusion equation will be derived which is a special case of a diffusion
equation with a time-dependent diffusivity. Therewith the simulation of
spreading of an elementary Gaussian is made easy as will be shown herein.
  With these tools one also accounts for Born's rule for multi-slit systems and
develops a set of current rules that directly leads to a new formulation of the
guiding equation equivalent to the original one of the de Broglie-Bohm theory.
As will be shown in this thesis, this tool reproduces Talbot patterns and
Talbot distance for an arbitrary multi-slit system.
  Moreover, the sweeper effect is shown to arise when the intensity relation of
two beams of a double-slit experiment exhibit a big difference. Then, the
low-intensity beam is pushed aside in a sense that its initial propagation
straight out of the slit is bent towards the side. A sideways screen as an
alternative measurement method is proposed.
