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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. This Demonstration shows the product ... , which depends on the angular quantum number ... , either an integer or a half-integer, ... and also depends on the magnetic quantum number ... , ... (there are ... values for ... ). Here it is provided that the actual quantum mechanical state is a simultaneous eigenket (eigenstate) of the operator ... and of the component ... ; the eigenvalues of ... are ... , where ... is reduced Planck's constant ... . The uncertainty product ... is an increasing function of the quantum number ... . Furthermore, it can be seen that (for fixed ... ) such states with ... are minimum-uncertainty product states; otherwise states with ... or ... have maximum uncertainty products.

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      EUN,LOM,LRE4,work-cmr-id:262139,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/UncertaintyProductForAngularMomentumComponents/,ilox,learning resource exchange,LRE metadata application profile,LRE

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