  Principle of locality means that any local change (perturbation) of the
stationary state wave function field propagates with finite speed, and
therefore reaches distant regions of the field with time delay.
  If a one-particle or multi-particle non-relativistic quantum system is
initially in a stationary state, and its wave function field is locally
perturbed, then perturbed and non-perturbed sub-regions appear in the region.
According to Schr\"odinger equation, borders of the perturbed sub-region
propagate with infinite speed, and the perturbation instantaneously affects all
infinite region. It means that Schr\"odinger equation predicts infinite speed
of the wave function perturbations propagation. This feature of classical
Schr\"odinger equation is traditionally interpreted as non-locality of quantum
mechanics. From physical point of view, such mathematical behavior of
Schr\"odinger equation solutions is questionable because it is difficult to
accept that in real world infinite physical objects can instantaneously appear.
  We introduce a hypothesis that in reality speed of propagation of the
perturbed sub-region borders is equal speed of light. On this basis we develop
and analyze a finite propagation speed concept for non-relativistic quantum
equations. It leads to local interpretation of non-relativistic quantum
mechanics consistent with principle of locality and free of local hidden
variables. The theory is applied to analysis of Einstein-Podolsky-Rosen (EPR)
paradox, entanglement and properties of perturbed matter waves. We proved that
formulated theory agrees with results of classical experiments on electron
matter waves diffraction.
