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# hw1 - PHY 4604 Spring 2012 Homework 1 Due at the start of...

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PHY 4604 Spring 2012 – Homework 1 Due at the start of class on Friday, January 20. No credit will be available for homework submitted after the start of class on Wednesday, January 25. Answer all four 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. This assignment is primarily designed to provide practice with standard mathematical tech- niques encountered in wave mechanics. You may ﬁnd useful the following integrals: Z 0 x 2 n exp( - x 2 /a 2 ) dx = π (2 n )! n ! ± a 2 ² 2 n +1 , Z 0 dx ( a 2 + x 2 ) n +1 = π (2 n - 1)!! 2 n +1 a 2 n +1 n ! where a is real, n is a non-negative integer, n != n · ( n - 1)! with 0! = 1, and n !! = n · ( n - 2)!! with 0!! = ( - 1)!! = 1. 1. Consider the wave function Ψ( x, t )= A exp[ - ( x 2 / 2 a 2 + iEt/ ~ )] , (1) where a is a real length scale and E isarea lenergy

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hw1 - PHY 4604 Spring 2012 Homework 1 Due at the start of...

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