  The notion of a double well potential typically involves two regions of space
separated by a repulsive potential barrier. The solution is a wave function
that is suppressed in the barrier region and localized in the two surrounding
regions. Remarkably, we illustrate that similar solutions can be achieved using
an attractive "barrier" potential (a "quantum moat") instead of a repulsive one
(a "quantum wall"). The reason this works is intimately connected to the
concepts of "orthogonalized plane waves" and the pseudopotential method, both
originally used to understand electronic band structures in solids. While the
main goal of this work is to use a simple model to demonstrate the barrier-like
attribute of a quantum moat, we also show how the pseudopotential method is
used to greatly improve the efficiency of constructing wave functions for this
system using matrix diagonalization.
