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The solution to a problem in quantum mechanics is generally a linearsuperposition of states. The solutions for double well potentials epitomizethis property, and go even further than this: they can often be described by aneffective 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 theparticle is on the other side. Then the ground state remains a linearsuperposition of these two macroscopic-like states. In this paper we illustratethat this property is achieved similarly with an attractive potential thatseparates two regions of space, as opposed to the traditionally repulsive one.In explaining how this comes about we revisit the concept of "orthogonalizedplane waves," first discussed in 1940 to understand electronic band structurein solids, along with the accompanying concept of a pseudopotential. We showhow these ideas manifest themselves in a simple double well potential, whose"barrier" consists of a moat instead of the conventional wall.

Double well potentials with a quantum moat barrier or a quantum wall barrier give rise to similar entangled wave functions