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Unformatted text preview: PHY 4604 Fall 2009 – Homework 2 Due at the start of class on Friday, September 18. No credit will be available for homework submitted after the start of class on Wednesday, September 23. Answer all three questions. Please write neatly and include your name on the front page of your answers. You must also clearly identify all your collaborators on this assignment. To gain maximum credit you should explain your reasoning and show all working. Your may find useful the following mathematical results: sin 2 x + cos 2 x = 1 , 2 sin ax cos bx = sin( a + b ) x + sin( a b ) x, Z x sin x dx = sin x x cos x Z x 2 cos x dx = ( x 2 2) sin x + 2 x cos x, Z x 2 cos 2 x dx = x 3 6 + 2 x 2 1 8 sin 2 x + x 4 cos 2 x 1. An infinite square well confines a particle of mass m to the region a/ 2 < x < a/ 2. (This well is shifted compared to the one considered in class.) The particle’s spatial wave functions can be written ψ n ( x ) = p 2 /a cos( nπx/a ) for n = 1, 3, 5, . . . , and ψ n ( x ) = p 2 /a sin( nπx/a ) for n = 2, 4, 6, . . . . Therefore, ψ n ( x ) = ( 1) n 1 ψ n ( x ), a relationship that holds (up to a relabeling n → n 1 in cases where the ground state is labeled n = 0 rather than n = 1) for any potential satisfying V ( x ) = V ( x )....
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This note was uploaded on 12/15/2011 for the course PHY 4604 taught by Professor Field during the Fall '07 term at University of Florida.
 Fall '07
 Field
 mechanics, Work

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