2011 June | Quantum Science Philippines

## Archive for June, 2011

### Proving Vector Identity Involving the Unit Vector Using the Levi-Civita and the Kronecker Delta

Wednesday, June 29th, 2011

*author: Michelle R. Fudot   Prove: ___________________________________________________________ Proof: First, we define the following vectors as: ; ; and Now,  if we let i=k, then . Furthermore, Now, the derivative of orthonormal basis , that is, and the derivative of a coordinate X, . Also, , thus = = = = It is noted that . […]

### Vector Analysis

Wednesday, June 29th, 2011

Prove: where:     Sol’n:   then:             or

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### Curl of the Gradient of a Scalar

Wednesday, June 29th, 2011

proof that the curl of the gradient of a scalar function is equal to zero let and

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### Proving Vector Identity Using Levi-Civita Symbol

Tuesday, June 28th, 2011

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,

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

Tuesday, June 28th, 2011

By 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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