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- W3037661937 abstract "We analyze general uncertainty relations and we show that there can exist such pairs of non-commuting observables [Formula: see text] and [Formula: see text] and such vectors that the lower bound for the product of standard deviations [Formula: see text] and [Formula: see text] calculated for these vectors is zero: [Formula: see text]. We also show that for some pairs of non-commuting observables the sets of vectors for which [Formula: see text] can be complete (total). The Heisenberg, [Formula: see text], and Mandelstam–Tamm (MT), [Formula: see text], time–energy uncertainty relations ([Formula: see text] is the characteristic time for the observable [Formula: see text]) are analyzed too. We show that the interpretation [Formula: see text] for eigenvectors of a Hamiltonian [Formula: see text] does not follow from the rigorous analysis of MT relation. We show also that contrary to the position–momentum uncertainty relation, the validity of the MT relation is limited: It does not hold on complete sets of eigenvectors of [Formula: see text] and [Formula: see text]." @default.
- W3037661937 created "2020-07-02" @default.
- W3037661937 creator A5034370503 @default.
- W3037661937 date "2020-06-25" @default.
- W3037661937 modified "2023-09-26" @default.
- W3037661937 title "Remarks on the uncertainty relations" @default.
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- W3037661937 doi "https://doi.org/10.1142/s0217732320502193" @default.
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