Unformatted text preview: x ) A = R i 2 π sin 2 ( x ) d x = √ π Since || sin( x ) || is not one, sin( x ) is not a normalized function on 0 ≤ x ≤ 2 π . If you divide by its norm, i.e. by √ π , however, || sin( x ) / √ π || = R i 2 π (sin( x ) / √ π )(sin( x ) / √ π ) d x = r π/π = 1 2.3.6 Solution dot-f Question: Verify that the most general multiple of sin( x ) that is normalized on the interval ≤ x ≤ 2 π is e i α sin( x ) / √ π where α is any arbitrary real number. So, using the Euler formula,...
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- Fall '11
- mechanics, Sin, Complex number, Leonhard Euler, π