 Lowest parity states of a symmetric double well

For normalized localized states related by reflection and real overlap $s=⟨{\varphi }_L|{\varphi }_R⟩$, the displayed superpositions are normalized even and odd states. The even state is lower for the lowest tunnelling pair; the odd state has one central node. Small overlap explains nearly identical probability densities in the two distant wells, but the relative phase remains different. A localized one-well state is a superposition of the pair rather than an exact stationary parity eigenstate.