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Cited by 5,409Quantum Mechanics and ApplicationsSpectral Theory in Mathematical PhysicsAtomic and Molecular Physics

The Principles of Quantum Mechanics

Dirac, P. A. M., Polkinghorne, J. C.·1958·Physics Today
DOI 10.1063/1.3062610
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Abstract

We are now going to put some order in our ideas and do theoretical physics. During the years 1925 to 1927, quantum mechanics took shape and accumulated successes. But three persons, and not the least, addressed the question of its structure. In Zürich there was Erwin Schrödinger, in Göttingen David Hilbert, and in Cambridge Paul Adrien Maurice Dirac.KeywordsHilbert SpaceQuantum MechanicScalar ProductState VectorComplex Vector SpaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • For Bychkov-Rashba spin splitting, the spin energies are E = ±αk, and at k=0 there is no gap (ΔE=0).

    “One can easily solve the eigenenergy equation and obtain the spin energies E = ± αk . The important difference with the case considered above is that here at k = 0 there is ∆ E = 0, i.e. there is no gap.”

    From Zitterbewegung (trembling motion) of electrons in semiconductors: a review (2011) · cites this paper as [28]

  • The modern reading of the position-momentum uncertainty relation is that no measurement can fix both a quantum particle's position and momentum with unlimited precision at the same time.

    “In its modern interpretation the uncertainty relation for position and momentum expresses the fact that the position and the momentum of a quantum particle cannot be measured simultaneously with infinite precision [6].”

    From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [6]

  • Unitary evolution on a normalized state vector is the correct physical description of an isolated system evolving in time according to quantum mechanics.

    “This unitary evolution on a normalized state vector is known to be the correct physical description of an isolated system evolving in time according to the laws of quantum mechanics[1].”

    From Elementary gates for quantum computation (1995) · cites this paper as [1]

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Authors
Dirac, P. A. M., & Polkinghorne, J. C.
Affiliations
University of Edinburgh (GB)
Venue
Physics Today
Publisher
AIP Publishing
Published
1958-06-01
Volume
11
Issue
6
Pages
32-33
ISSN
  • 0031-9228 (ISSN-L)
  • 1945-0699
DOI
10.1063/1.3062610
OpenAlex
W1965075382
Cited by
5,409
References
0
Citations by year
2026: 52 · 2025: 43 · 2024: 53 · 2023: 36 · 2022: 54 · 2021: 171 · 2020: 272 · 2019: 168 · 2018: 139 · 2017: 146 · 2016: 176 · 2015: 191 · 2014: 195 · 2013: 199 · 2012: 209
Type
book review
Language
en
Update notices
correction (1958-07-01)
Open access
closed
Locations
Physics Today (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Atomic and Molecular Physics
Keywords
quantum mechanics, Hilbert spaces, state vector, inner product, complex vector spaces, Erwin Schrödinger, DIRAC, Hilbert, history of quantum mechanics

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