Limitations of standard quantum mechanics caused by its current mathematical model and a way out

The standard quantum-mechanical model is based on the solutions of time-independent Schroedinger equation and does not allow to describe in principle any characteristic changing during the time evolution. This paper discusses how an evolving system can, however, described correspondingly in the framework of an extended Hilbert structure following from the time-dependent Schroedinger equation if a consequent approach is applied to. In such a structure some further operators must be added to the common mutually commuting set to define fully the properties of a physical system. The simplest system consisting of two free particles must be then characterized, e.g., by an impact-parameter value in addition to usual quantities. That has fundamental impact on the interpretation of any measurement process and of the EPR problem, as Bell inequalities are not more applicable to the corresponding coincidence experiments