hwsol6 - Physics 31 Spring, 2008 Solution to HW #6 Problem...

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Unformatted text preview: Physics 31 Spring, 2008 Solution to HW #6 Problem A The wave function of a particle is given by ( x ) = N exp " x 3 . 1915 A 2 # (When you evaluate this function, take all distances x in A.) (e) Use the exact formula to evaluate x for this wave func- tion: x = p x 2 x 2 . Compare your answer to your estimate in part (d). Hint: You need the integral R x 2 exp( ax 2 ) dx = 1 4 p /a 3 , but you do not need the integral R x exp( ax 2 ) dx = 1 / (2 a ). Why not? We can evaluate x rigorously using the expression x = p x 2 x 2 . Note that the average value x = 0. This result follows from the integral expression x = Z x ( x ) 2 dx = N 2 Z x exp 2 x b 2 dx which is zero because the integrand is an odd function [that is, f ( x ) = f ( x ), so the contributions to the integral from x < 0 and x > 0 exactly cancel]....
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This note was uploaded on 08/06/2008 for the course PHYS 31 taught by Professor Hickman during the Spring '08 term at Lehigh University .

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