05_03_30 - Georg.Hoffstaetter@Cornell.edu 110 Projection...

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Unformatted text preview: Georg.Hoffstaetter@Cornell.edu 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 -- + = -- = = 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 -- + = = x t x ) , ( 2 | ) , ( | y probabilit with t x x n x x n = ) ( Measurement: Projection amplitude: Ket vector: = x x x all 03/30/2005 Georg.Hoffstaetter@Cornell.edu 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 + = - = = n x in n L e a x f 2 ) ( - =-- = n x m n i n x im L L e a e x f 2 2 ) ( ) ( m x im L a dx e x f L L L = -- 2 2 2 ) ( 1 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...
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05_03_30 - Georg.Hoffstaetter@Cornell.edu 110 Projection...

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