Abstract
It is shown that in scattering theory, the Heisenberg relation has the form\(\left\langle {\psi , H\psi } \right\rangle \Delta Q_{\Omega _ \pm ^ * \psi }^2 \geqslant \frac{9}{4}h^2\) for a wide class of potentials.H is the Hamiltonian of scattered particles, Ψ is a scattering state, and Ω± are wave operators. We discuss the interpretation of the obtained inequality and its entropic formulation.
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Grabowski, M. Remarks on the uncertainty relation in scattering theory. Letters in Mathematical Physics 13, 153–156 (1987). https://doi.org/10.1007/BF00955205
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DOI: https://doi.org/10.1007/BF00955205