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Uncertainty Relations

Chapter
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Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Abstract

In this chapter, we show how uncertainty relations arise naturally from quantum theory for position and momentum, time and energy, and so on. We explore the meaning of these relations and apply them to the quantum mechanical description of the pendulum. Finally, we show how we can use entanglement to enhance the precision of measurements.

Supplementary material

460544_1_En_9_MOESM1_ESM.zip (504 kb)
Supplementary material 1: Daisy-chaining two Stern–Gerlach experiments (zip 503 KB)
460544_1_En_9_MOESM2_ESM.zip (684 kb)
Supplementary material 2: Daisy-chaining three Stern–Gerlach experiments (zip 683 KB)
460544_1_En_9_MOESM3_ESM.zip (124 kb)
Supplementary material 3: The pendulum (zip 123 KB)
460544_1_En_9_MOESM4_ESM.zip (740 kb)
Supplementary material 4: The coherent state for the pendulum (zip 739 KB)
460544_1_En_9_MOESM5_ESM.zip (382 kb)
Supplementary material 5: Measuring the spin direction on N separate spins (zip 381 KB)
460544_1_En_9_MOESM6_ESM.zip (392 kb)
Supplementary material 6: Measuring the spin direction on N entangled spins (zip 391 KB)

References

  1. J.S. Bell, On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964)MathSciNetCrossRefGoogle Scholar
  2. A. Einstein, B. Podolsky, N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSCrossRefGoogle Scholar
  3. W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik 43, 172 (1927)ADSCrossRefGoogle Scholar
  4. M. Holland, K. Burnett, Interferometric detection of optical phase shifts at the Heisenberg limit. Phys. Rev. Lett. 71, 1355 (1993)ADSCrossRefGoogle Scholar
  5. H.P. Robertson, The uncertainty principle. Phys. Rev. 34, 163 (1929)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of SheffieldSheffieldUK

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