  In classical mechanics, a particle cannot escape from an unbounded potential
well. Naively, one would expect a similar result to hold in wave mechanics,
since high barriers make tunneling difficult. However, this is not always the
case and it is known that wave delocalization can arise in certain models with
incommensurate unbounded potentials sustaining critical states, i.e. states
neither fully extended nor fully localized. Here we introduce a different and
broader class of unbounded potentials, which are not quasi-periodic and do not
require any specially-tailored shape, where wave delocalization is observed.
The results are illustrated by considering light dynamics in synthetic photonic
lattices, which should provide a feasible platform for the experimental
observation of wave delocalization in unbounded potentials.
