05_03_30

# 05_03_30 - [email protected] 110 Projection...

This preview shows pages 1–3. 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: [email protected] 110 Projection probabilities and ket vectors 2 1 1 | | y probabilit with A E 2 2 1 1 2 1 ) , ( A e A e t x t i t i E E -- Φ + Φ = Ψ ∫ ∞ ∞-- Ψ Φ = Ψ = dx t x x A e t i E ) , ( ) ( 1 * 1 1 1 ¡ 2 1 2 1 2 1 A e A e t i t i E E ¢ ¢-- + = Ψ Ψ = Ψ x t x ) , ( 2 | ) , ( | y probabilit with t x x Ψ n x x n = Φ ) ( Measurement: Projection amplitude: Ket vector: ∑ Ψ = Ψ x x x all 03/30/2005 [email protected] 111 03/30/2005 Fourier Series Any “well behaved” periodic function f(x)=f(x+L) can be written as the sum of elementary periodic functions-2-1 1 2-3-2-1 1 2 (L) f(x) ) sin( ) cos( 2 2 2 x n i x n e L L x in L π π π + = ∑ ∞-∞ = = n x in n L e a x f π 2 ) ( ∑ ∞-∞ =-- = n x m n i n x im L L e a e x f π π 2 2 ) ( ) ( m x im L a dx e x f L L L = ∫-- 2 2 2 ) ( 1 π Real functions f(x): * m m a a =- ∑ ∑ ∑ ∞ = ∞ = ∞ =- + = + = 1 2 1 2 1 ) sin( ] Im[ 2 ) cos( ] Re[ 2 ] Re[ 2 ) ( 2 n L n n L n n x...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

05_03_30 - [email protected] 110 Projection...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online