  Following Max Planck's hypothesis of quanta (quant-ph/0012069) and the matter
wave idea of Louis de Broglie (quant-ph/9911107), Erwin Schroedinger proposed,
at the beginning of 1926, the concept of wavefunction and wave equation for it.
Though endowed with a realistic undular interpretation by its father, the
wavefunction could not be considered as a real "matter wave" and has been
provided with only abstract, formally probabilistic interpretation. In this
paper we show how the resulting "mysteries" of usual theory are solved within
the unreduced, dynamically multivalued description of the underlying,
essentially nonlinear interaction process (quant-ph/9902015, quant-ph/9902016),
without artificial modification of the Schroedinger equation. The latter is
rigorously derived instead as universal expression of unreduced interaction
complexity. Causal, totally realistic wavefunction is obtained as a dynamically
probabilistic intermediate state of a simple system with interaction performing
dynamically discrete transitions between its localised, incompatible
"realisations" ("corpuscular" states). Causal wavefunction and Schroedinger
equation are then extended to arbitrary level of world dynamics. We outline
some applications of the obtained causal description, such as genuine quantum
chaos (quant-ph/9511034-36) and realistic quantum devices (physics/0211071),
and emphasize the basic difference of the proposed dynamically multivalued
theory from dynamically single-valued imitations of causality and complexity.
The causally complete wavefunction concept, representing the unified essence of
unreduced (multivalued) complex dynamics, provides a clear distinctive feature
of realistic science, absent in any its unitary imitation.
