Roel N. Baybayon MSPhysics1 ————————————————————————————————– We are going to prove the following vector identity using Levi-Civita symbol: Solution: Let , , , . Then, By definition: We have to let m=n so that, Levi-Civita symbol can be expressed in terms of Kronecker delta given by: Thus,

### Proving Vector Identity Using Levi-Civita Symbol

Tuesday, June 28th, 2011Posted in Electrodynamics, Quantum Science Philippines **|** 1 Comment »

### Verifying vector formulas using Levi-Civita: (Divergence & Curl of normal unit vector n)

Tuesday, June 28th, 2011By Sim P. Bantayan, MS Physics I, MSU-IIT Let , and where and . 1. Prove that . Proof: Now, . Since i=j for the divergence of normal unit vector n, but (i=j). Moreover, for three dimensions, , so Therefore, . 2. Prove that . Proof: . Since i=j for the curl of normal unit vector n, […]

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### Prove that the Divergence of a Curl is Zero by using Levi Civita

Tuesday, June 28th, 2011Author: Kayrol Ann B. Vacalares The divergence of a curl is always zero and we can prove this by using Levi-Civita symbol. The Levi-Civita symbol, also called the permutation symbol or alternating symbol, is a mathematical symbol used in particular in tensor calculus. Prove that: = 0 Proof: Let: and To show that: = 0 First, Here are the possible […]

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### Proving Vector Formula with Kronecker Delta Function and Levi-Civita Symbol

Tuesday, June 28th, 2011Applying and in Proving the Vector Formula: By: Quennie J. Paylaga Prove: using Kronecker Delta Function and Levi-Civita Symbol. To prove this, we let We can write the expression for in summation form as: where where i, j, l are dummy summation variables. Each of which can be any letter […]

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### Verifying a Vector Identity (BAC-CAB) using Levi-Civita

Monday, June 27th, 2011Author: CHRISTINE ADELLE L. RICO Here is another method of verifying a vector formula using the Levi-Civita symbol. Levi-Civita symbol is a tensor of rank three and is defined by +1 if the indices are in even permutation of , -1 if the indices are in odd permutation, and 0 if any two indices are […]

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