  We study heterogeneous distribution of gains in neural fields using
techniques of quantum mechanics by exploiting a relationship of our model and
the time-independent Schr\"{o}dinger equation. We show that specific
relationships between the connectivity kernel and the gain of the population
can explain the behavior of the neural field in simulations. In particular, we
show this relationships for the gating of activity between two regions (step
potential), the propagation of activity throughout another region (barrier)
and, most importantly, the existence of bumps in gain-contained regions (gain
well). Our results constitute specific predictions that can be tested in vivo
or in vitro.
