Paper detail

On formation of long-living states

The motion of a particle in the potential well is studied when the particle is attached to the infinite elastic string. This is generic with the problem of dissipative quantum mechanics investigated by Caldeira and Leggett. Besides the dissipative motion there is another scenario of interaction of the string with the particle attached. Stationary particle-string states exist with string deformations accompanying the particle. This is like polaronic states in solids. Our polaronic states in the well are non-decaying and with continuous energy spectrum. Perhaps these states have a link to quantum electrodynamics. Quantum mechanical wave function, singular on some line, is smeared out by electron "vibrations" due to the interaction with photons. In those anomalous states the smeared singularity position would be analogous to the place where the particle is attached to the string.