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hwk6 - x in the particles position Hint Do not do any...

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Physics 31: Homework #6 Due Thursday, March 13, 2008 Parts (a)–(d) of Problem A are the same as Problem A from Homework #5. This week, just do part (e). Problem A: The wave function of a particle is given by ψ ( x ) = N exp x 3 . 1915 ˚ A 2 (When you evaluate this function, take all distances x to be in ˚ A.) (a) What is the correct numerical value of the normalization constant N ? Hint: You must explicitly evaluate N . (b) Make a plot of ψ ( x ) and ψ ( x ) 2 . Indicate numerical values. (c) Estimate the probability that a measurement of the particle’s position gives a value between x = 1 . 45 ˚ A and x = 1 . 55 ˚ A. (d) Use the sketch you made in part (b) to estimate the uncertainty ∆
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Unformatted text preview: x in the particles position. Hint: Do not do any integrals to answer this part of the question. (e) Use the exact formula to evaluate x for this wave function: x = q 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 q /a 3 , but you do not need the integral R x exp( ax 2 ) dx = 1 / (2 a ). Why not? Do the following problems in Beiser: Chapter 5: 2, 5, 8, 10 (You will need the integral table from last weeks assignment.)...
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