Position-momentum uncertainty products

We point out two interesting features of position-momentum uncertainty product: $U=Δx Δp$. We show that two special (non-differentiable) eigenstates of the Schr{ö}dinger operator with the Dirac Delta potential $[V(x)=-V_0 δ(x)],V_0>0$, also satisfy the Heisenberg's uncertainty principle by yielding $U> \frac{\hbar}{2}$. One of these eigenstates is a zero-energy and zero-curvature bound state.

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