# Einstein Summation and Levi-Civita Tensor

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.

http://farside.ph.utexas.edu/teaching/qmech/Quantum/node80.html

© BrainMass Inc. brainmass.com October 10, 2019, 7:53 am ad1c9bdddfhttps://brainmass.com/physics/mathematical-physics/einstein-summation-levi-civita-tensor-599170

#### Solution Preview

Let define two vectors:

The cross productis:

(1.1)

Now if we define then:

(1.2)

We know that

(1.3)

Then:

(1.4)

We note that:

(1.5)

So if we ...

#### Solution Summary

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

$2.19