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Unformatted text preview: PHY 4604 Fall 2010 Homework 2 Due at the start of class on Friday, September 17. No credit will be available for homework submitted after the start of class on Wednesday, September 22. Answer both 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 x cos y = sin( x- y ) + sin( x + y ) 2 sin x sin y = cos( x- y ) + cos( x + y ) , 2 cos x cos y = cos( x- y )- cos( x + y ) Z x sin x dx = sin x- x cos x, Z x cos x dx = x sin x + cos x, Z sin 2 x dx = x 2- 1 4 sin 2 x Z x 2 cos x dx = ( x 2- 2) sin x + 2 x cos x, Z x 2 sin 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 particles spatial wave functions can be written n ( x ) = p 2 /a cos( nx/a ) for n = 1, 3, 5, . . . , and n ( x ) = p 2 /a sin( nx/a ) for n = 2, 4, 6, . . . . Therefore, n (- x ) = (- 1) n- 1 n ( x ), a relationship that holds [with (- 1) n- 1 replaced by (...
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