A quantum moat barrier, realized with a finite square well

The notion of a double well potential typically involves two regions space separated by repulsive barrier. ground state
 is wave function that suppressed in the barrier region and localized surrounding regions. We illustrate an attractive (a quantum moat) with finite non-zero width also acts as barrier, using simple square model. show how pseudopotential method both explains role greatly improves efficiency constructing functions for this system matrix diagonalization. With simplified model we provide introduction to ideas used simplify calculations solids, where place potential, multiple potentials occur periodic array.