  The solution to a problem in quantum mechanics is generally a linear
superposition of states. The solutions for double well potentials epitomize
this property, and go even further than this: they can often be described by an
effective model whose low energy features can be described by two states ---
one in which the particle is on one side of the barrier, and a second where the
particle is on the other side. Then the ground state remains a linear
superposition of these two macroscopic-like states. In this paper we illustrate
that this property is achieved similarly with an attractive potential that
separates two regions of space, as opposed to the traditionally repulsive one.
In explaining how this comes about we revisit the concept of "orthogonalized
plane waves," first discussed in 1940 to understand electronic band structure
in solids, along with the accompanying concept of a pseudopotential. We show
how these ideas manifest themselves in a simple double well potential, whose
"barrier" consists of a moat instead of the conventional wall.
