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 Schrödinger 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.