# Uncertainty Product for Angular Momentum Components

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In quantum physics the (orbital- or spin-) angular momentum components , , and are represented by *noncommutating* Hermitian operators. Therefore, no quantum state exists with the property that two of the uncertainties , , vanish simultaneously.

Contributed by: Reinhard Tiebel (April 2011)

Open content licensed under CC BY-NC-SA

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## Details

The general uncertainty relation for any noncommutating operators , reads , where is the expectation value of the commutator *. *In the special case of angular momentum operators , we obtain . In the common basis of , eigenstates, the desired uncertainty product can be calculated exactly: * *and plotted in the diagram.

References

[1] L. D. Landau and E. M. Lifschitz, *Quantum Mechanics*, Reading MA: Addison–Wesley Publishing Company, 1958.

[2] J. J. Sakurai, *Modern Quantum Mechanics*, Reading MA: Addison–Wesley Publishing Company, 1995.

[3] P. Reineker, M. Schulz, and B. M. Schulz, *Theoretische Physik III: Quantenmechanik 1*, Berlin: Wiley–VCH, 2007.

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