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# ç¬¬22è®²å¸ƒæ´›èµ«ç”

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Unformatted text preview: 143 r ∆ r k ∆ k ∆ r ∆ k ∆ k ∆ r ( ) ( ) ( ) ' ' ' ' , E i t t e u ψ   ⋅ −     = = k k r k k r r (5-1) ( ) ' u k r k k ’ k k ’ k k ’ ' = + k k k k (5-1) E ( k ’ ) k ( ) ( ) ( ) ' E E E ≅ + ⋅ ∇ k k k k k (5-2) 2 2 x y z k k k   ∆ ∆   − ≤ ≤       (5-1) (5-2) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 , , k x y z E E i t i t x y z t d k d k d k t e u dk dk dk e ψ ψ ∆ ∆ ∆ + −∆ −∆ −∆   ∇     ⋅ − ⋅ −     ∆ ∆ ∆     −∆ −∆ −∆ = ≅ ∫ ∫ ∫ ∫ ∫ ∫ = = k k k k k k r k r k r r r (5-3) ( ) u k' r k ( ) u k r ( ) ( ) ( ) ( ) ( ) ( ) / 2 / 2 ' / 2 / 2 , k k k k k k E k E k E k ik x t ik x t ik x t k k x t u x e dk u x e e dk ψ       ∇ ∇ ∇       − − − ∆ ∆             −∆ −∆ = ≈ ∫ ∫ = = = ( ) ( ) ( ) ( ) ( ) sin 2 , 1 2 k k k E k ik x t k k k E k x t x t u x e E k x t i ψ ∇   −         ∇ ∆   −     =   ∇   −     = = = ( ) ( ) ( ) 2 2 2 2 2 2 2 1 sin 2 sin 1 2 x k k k x k E x t k X x,t u x u x X E x t k ψ       ∆ ∂     −   ∂      ...
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## This note was uploaded on 05/05/2010 for the course PHYSICS 111 taught by Professor Zhengxiang during the Spring '08 term at Peking Uni..

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ç¬¬22è®²å¸ƒæ´›èµ«ç”

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