Anomalous electron states

Abstract: By the certain macroscopic perturbations in condensed matter anomalous electron wells can be formed due to a local reduction of electromagnetic zero point energy. These wells are narrow, of the width $\sim 10^{-11}cm$, and with the depth $\sim 1MeV$. Such anomalous states, from the formal standpoint of quantum mechanics, correspond to a singular solution of a wave equation produced by the non-physical $\delta(\vec R)$ source. The resolution, on the level of the Standard Model, of the tiny region around the formal singularity shows that the state is physical. The creation of those states in an atomic system is of the formal probability $\exp(-1000)$. The probability becomes not small under a perturbation which rapidly varies in space, on the scale $10^{-11}cm$. In condensed matter such perturbation may relate to acoustic shock waves. In this process the short scale is the length of the standing de Broglie wave of a reflected lattice atom. Under electron transitions in the anomalous well (anomalous atom) $keV$ X-rays are expected to be emitted. A macroscopic amount of anomalous atoms, of the size $10^{-11}cm$ each, can be formed in a solid resulting in ${\it collapsed}$ ${\it matter}$ with $10^9$ times enhanced density.