Position-momentum uncertainty products

Abstract

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

Modified version, no Figures, one Table, 8 pages, to appear in Eur. J. Phys

References in corpus (1)

• Playing Quantum Physics Jeopardy with zero-energy eigenstates

Cited by in corpus (2)

• Building Confidence in the Dirac $\delta$-function
• Anti-symmetric square well and barrier potential between two rigid walls