A closer look at the uncertainty relation of position and momentum. (English) Zbl 1181.81010
Summary: We consider particles prepared by a single slit diffraction experiment. For those particles, the standard deviation \(\sigma_{p}\) of the momentum is discussed. We find out that \(\sigma_{p}=\infty \) is not an exception but a rather typical case. A necessary and sufficient condition for \(\sigma_{p}<\infty \) is given. Finally, the inequality \(\sigma_{p}\Delta x\geq \pi \hbar\) is derived and it is shown that this bound cannot be improved.
MSC:
| 81P15 | Quantum measurement theory, state operations, state preparations |
| 81S05 | Commutation relations and statistics as related to quantum mechanics (general) |
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