Lect14_Scattering - Scattering From a Potential Step...

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Lecture 14: Systematic Approach to 1D Scattering PHY851 Fall 2008 M. G. Moore Scattering From a Potential Step revisited Lets solve the step potential again, but with the possibility for left and right travelling incoming waves: E x V I I II x k i x k i I be ae x 1 1 ) ( ! + = " x k i x k i II de ce x 2 2 ) ( ! + = ( ) h I I I V E m E V iu V E u k ! ! + ! = 2 ) ( ) ( 1 V II ( ) h II II II V E m E V iu V E u k ! ! + ! = 2 ) ( ) ( 2 d c b a II I + = + ! = ) 0 ( ) 0 ( x=0 ( ) ( ) d c k b a k II I ! = ! " # = # 2 1 ) 0 ( ) 0 ( $
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Scattering Matrix The scattering matrix gives the outgoing amplitudes in terms of the incoming amplitudes: ! ! " # $ $ % = ! ! " # $ $ % d a S c b d c b a + = + ( ) ( ) d c k b a k ! = ! 2 1 d a c b + ! = ! d k a k c k b k 2 1 2 1 + = + ! ! " # $ $ % ! ! " # $ $ % = ! ! " # $ $ % ! ! " # $ $ % d a k k c b k k 2 1 2 1 1 1 1 1 ! ! " # $ $ % ! ! " # $ $ % ! ! " # $ $ % = ! ! " # $ $ % d a k k k k c b 2 1 1 2 1 1 1 1 1 ! ! " # $ $ % ! ! " # $ $ % ! ! " # $ $ % + = ! ! " # $ $ % d
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Lect14_Scattering - Scattering From a Potential Step...

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