p827aps1sola

p827aps1sola - a + b | Z a with A Z | W a = 0. In this...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Solution to the Second Part of Shankar, Problem 1.3.4 In my original solution, I misinterpreted the phrase “the fnal inequality.” The correct interpretation is that we should show that eq. (1.3.16) becomes an inequality iF and only iF | V a = a | W a , where a is a real and positive scalar. To prove this, we have to show that Re A V | W a = | V || W | iF and only iF | V a = a | W a with a real and positive. Now we can always write | V a = a | W
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a + b | Z a with A Z | W a = 0. In this Form, we have A W | V a = a A W | W a = a | W | 2 , (1) so Re A W | V a = Re A V | W a = (Re a ) | W | 2 . Also | V || W | = r | a | 2 | W | 2 + | b | 2 | Z | 2 ( | W | ) . (2) rom this, we can see that | V || W | = Re A W | V a only iF | b | = 0 and also iF Re a = | a | , i. e., iF a is real and positive. Q. E. D. 1...
View Full Document

This note was uploaded on 07/17/2008 for the course PHYS 827 taught by Professor Stroud during the Fall '07 term at Ohio State.

Ask a homework question - tutors are online