Asymmetric wave functions from tiny perturbations

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The quantum mechanical behavior of a particle in a double well defies our intuition based on classical reasoning. Not surprisingly, an asymmetry in the double well will restore results more consistent with the classical picture. What is surprising, however, is how a very small asymmetry can lead to essentially classical behavior. In this paper we use the simplest version of a double well potential to demonstrate these statements. We also show how this system accurately maps onto a two-state system, which we refer to as a `toy model'.