hw_solutions_2 - Homework Solutions # 2 (Liboff Chapter 4)...

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Unformatted text preview: Homework Solutions # 2 (Liboff Chapter 4) 4.5 (a) Given in book. (b) | ih | f i = a | i , where a = R dx * f . (c) h f | ih | f i . (d) h f | ih | i = h f | i . 4.8 g ( x ) = s 2 a X n a n sin nx a where a n = s 2 a Z a dx sin nx a x ( x- a ) e ikx = 1 2 i s 2 a Z a dx ( x 2- ax ) e i ( k + n a ) x- e- i ( k + n a ) x Now the tedious integration. Use I ( ) = Z a dx e ix = 1 i e ia- 1 Z a dx x e ix =- i I = 1 2 e ia- 1- ia e ia Z a dx x 2 e ix =- 2 I 2 = 2 i 3 e ia- 1 + 2 a 2 e ia- ia 2 e ia Afer a bunch of algebra Im not going to reproduce here, we get a n = s 2 a h (- 1) n e ika- 1 i " 1 ( k + n/a ) 3 )- 1 ( k + n/a ) 3 ) #- ia (- 1) n e ika " 1 ( k + n/a ) 2- 1 ( k- n/a ) 2 #- a 2 i h (- 1) n e ika- 1 i " 1 ( k + n/a ) 2- 1 ( k- n/a ) 2 # Phys 580 HW# 2 Solutions 1 4.9 || + || 2 = h + | + i = ( h | + h | )( | i + | i ) = h | i + h | i...
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hw_solutions_2 - Homework Solutions # 2 (Liboff Chapter 4)...

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