  Using the example of the Davydov soliton - a large acoustic polaron in one
dimension - we demonstrate that the electron wave function can be fissioned in
two or more long-lived, well-localized and spatially arbitrarily far separated
fragments. The phenomenon of wave function splitting is a result of the
electron-medium interaction, and takes place under a variety of conditions
provided the initial wave function of the electron is localized and has at
least one node.
