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
