# hw2 - 1 Phys6103 Homework set#2 1 Levi-Civ` ıta Practice...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Phys6103: Homework set #2 1. Levi-Civ` ıta Practice Evaluate the following expressions which exploit the Einstein summation convention. (a) δ ii (b) δ ij ² ijk (c) ² ijk ² ‘jk (d) ² ijk ² ijk 2. Vector Identities Use the Levi-Civit`a symbol to prove that (a) ( A × B ) · ( C × D ) = ( A · C )( B · D )- ( A · D )( B · C ) (b) ∇ · ( f × g ) = g · ( ∇ × f )- f · ( ∇ × g ) (c) ( A × B ) × ( C × D ) = ( A · C × D ) B- ( B · C × D ) A (d) The 2 × 2 Pauli matrices σ x , σ y , and σ z used in quantum mechanics satisfy σ i σ j = δ ij + i² ijk σ k . If a and b are ordinary vectors, prove that ( σ · a )( σ · b ) = a · b + i σ · ( a × b ) . 3. Delta Function Identities A test function as part of the integrand is required to prove any delta function identity. With this in mind, (a) Prove that δ ( ax ) = 1 | a | δ ( x ). (b) Use the identity in part (a) to prove that δ [ g ( x )] = X m 1 | g ( x m ) | δ ( x- x m ) where g ( x m ) = 0 ....
View Full Document

## This note was uploaded on 08/30/2011 for the course PHYS 6103 taught by Professor Grigoriev during the Summer '11 term at Georgia Tech.

### Page1 / 2

hw2 - 1 Phys6103 Homework set#2 1 Levi-Civ` ıta Practice...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online