Quantum unbinding in potentials with 1/r P tails

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Abstract
Potentials with repulsive power behavior at large distances may or may not have a zero-energy bound state, depending only on the power p and, if p=2, the strength. For the case of no zero-energy bound state, we further study how the state unbinds as the attractive, small r part of the potential is tuned to let the binding energy go to zero. Although motivated by the physics of wetting, this problem is well suited for senior or graduate level quantum mechanics courses by giving a novel perspective of solutions to one-dimensional Schroedinger equations.

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