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Unformatted text preview: PHY 4604 Fall 2008 – Homework 1 Due at the start of class on Friday, September 5. No credit will be available for homework submitted after the start of class on Wednesday, September 10. 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: for real a and n = 0 , 1 , 2 , 3 , . . . , Z ∞ x 2 n exp(- x 2 /a 2 ) dx = √ π (2 n )! n ! a 2 2 n +1 Z ∞ dx ( a 2 + x 2 ) n +1 = π (2 n- 1)!! 2 n +1 a 2 n +1 n ! where n ! = n · ( n- 1)! with 0! = 1, and n !! = n · ( n- 2)!! with 0!! = (- 1)!! = 1. 1. We have not yet tackled the task of solving the Schr¨ odinger wave equation for any specific potential V ( x, t ). This question addresses the “reverse engineering” process of)....
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