Uncertainty Relations

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


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


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of SheffieldSheffieldUK

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