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    Einstein Summation and Levi-Civita Tensor

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    Please help answer this question. It requires you to give proof that two definitions of angular momentum are equal.

    The question is in the attachment. It is taken from this site.


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    Solution Preview

    Let define two vectors:

    The cross productis:

    Now if we define then:
    We know that
    We note that:
    So if we ...

    Solution Summary

    The solution shows how Levi-Civita tensor and Einstein summation help simplify the cross product expression.