Anomalies in non-relativistic quantum mechanics

The violation of some formal relations (anomalies) for the system of non-relativistic fermi-particles is shown to appear when a singularity of the potential is rather strong. For different singularity types (in part for Coulomb potential) the anomalies associated with the system energy and total number of particles are calculated. These anomalies may be useful in the semiclassical description of electron-nuclear systems.