05_03_18 - x = -) ( ) ( * , = = L R y x = x A x...

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Georg.Hoffstaetter@Cornell.edu 99 Quantum amplitudes for circular polarization 03/18/2005 The field of any plane light wave with frequency Q can be written as The Intensity in the R channel after an R/L analyzer: Intensity in the L channel: The corresponding state vector describes a photon which is in the state with probability and in the state with probability . The interferences of the photons correspond to the interferences of the field when the phases and the probability amplitudes are chosen according to the amplitudes and phases of the filed components by using complex quantum amplitudes ] ) Re[( ) ( 2 2 t z k i L e i e R e i e e B B E y x y x ϖ - + - + = * 2 2 * 4 1 2 ) ( 2 ] 2 [ 2 ] Re[ 2 R R t e i e e i e R R t t z k i R e i e R B B B B e B I y x y x y x = = + - - - * L L L B B I R | 2 | | R B L | 2 | | L B L R B L B R + = Ψ | | |
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Georg.Hoffstaetter@Cornell.edu 100 03/18/2005 Formal correspondence to polarization states y x A y A x + = Ψ The expansion amplitudes are found by projections; they are projection amplitudes. dx x f x A n n - Φ = ) ( ) ( * = Φ = N n n n A x x f 0 ) ( ) ( nm m n dx x
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Unformatted text preview: x = -) ( ) ( * , = = L R y x = x A x Polarization states Stationary states of the wave function Orthogonality Orthogonality Completeness: Every states can be described in terms of the basis states. Due to this correspondence, also the stationary states of the wave function are written as ket vector : with ) ( = m n n x n f n A A n f n N n n = = = with Georg.Hoffstaetter@Cornell.edu 101 03/18/2005 Physical correspondence to polarization states y x A y A x + = With probability * n n n A A P = = = N n n n A x x f ) ( ) ( Polarization states States of the wave function 2 * = = x A A P x x x x ) ( x n With probability Analyzers: can separate the components of the different basis states x Momentum analyzer Energy levels Measurement: changes the state of the quantum particle. 1 2 = = N n n A...
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05_03_18 - x = -) ( ) ( * , = = L R y x = x A x...

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