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Cited by 1,877Quantum Mechanics and ApplicationsNoncommutative and Quantum Gravity TheoriesSpectral Theory in Mathematical Physics

The uncertainty principle

Robertson, H. P.·1929·Physical Review
DOI 10.1103/physrev.34.163
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Crossref · 10.1103/physrev.34.163

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  • Robertson generalized relation (2) to classical observables A and B, i.e. functions of canonically conjugate coordinates and momenta, for pure quantum states.

    “A generalization of relation (2) to the case of 'classical' observables A and B , i.e., some functions of the canonically conjugate coordinates and momenta, was made by Robertson [5] (for pure quantum states):”

    From Uncertainty relations: a small zoo of remarkable inequalities discovered since 1927 (2025) · cites this paper as [5]

  • Robertson gave the same inequality (4) in a different but equivalent form.

    “The same inequality (4) was given by Robertson [8], but he wrote the right-hand side in a different form, which is equivalent to G 2 AB ≡ ∣ ∣ ∣ 〈 ( δ ˆ A )( δ ˆ B ) 〉∣ ∣ ∣ 2 .”

    From Uncertainty relations: a small zoo of remarkable inequalities discovered since 1927 (2025) · cites this paper as [8]

  • Bohr and Robertson placed the position-momentum uncertainty relation on solid grounds.

    “While the uncertainty relation for position and momentum was quickly put on solid grounds by Bohr [4] and Robertson [5]”

    From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [5]

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Authors
Robertson, H. P.
Affiliations
Princeton University (US)
Corresponding author
Robertson, H. P.
Venue
Physical Review
Publisher
American Physical Society (APS)
Published
1929-07-01
Volume
34
Issue
1
Pages
163-164
ISSN
0031-899X (ISSN-L)
DOI
10.1103/physrev.34.163
OpenAlex
W2042601507
Cited by
1,877
References
1
Citations by year
2026: 75 · 2025: 117 · 2024: 121 · 2023: 138 · 2022: 119 · 2021: 110 · 2020: 118 · 2019: 103 · 2018: 98 · 2017: 89 · 2016: 94 · 2015: 68 · 2014: 74 · 2013: 80 · 2012: 60
FWCI
0.66
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Physical Review (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
Keywords
uncertainty principle, quantum mechanics

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