HW1 solutions - Physics 4120 Spring 2008 Homework #1...

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Unformatted text preview: Physics 4120 Spring 2008 Homework #1 Solutions 1) 2)This problem is much easier if you use a spreadsheet rather than do every calculation by hand. J n(j) P(j) j*P(j) j j^2 j^2*P(j) j^2 j^2*P(j) 17 1 0.038462 0.653846-4.5 20.25 0.778846 289 11.11538 18 3 0.115385 2.076923-3.5 12.25 1.413462 324 37.38462 20 2 0.076923 1.538462-1.5 2.25 0.173077 400 30.76923 21 4 0.153846 3.230769-0.5 0.25 0.038462 441 67.84615 22 8 0.307692 6.769231 0.5 0.25 0.076923 484 148.9231 23 5 0.192308 4.423077 1.5 2.25 0.432692 529 101.7308 24 2 0.076923 1.846154 2.5 6.25 0.480769 576 44.30769 25 1 0.038462 0.961538 3.5 12.25 0.471154 625 24.03846 Sum: 26 1 21.5 3.865385 466.1154 N <j> ^2 <j^2> a) From our spreadsheet calculation, <j> = 21.5 b) j for each j is given in the spreadsheet above c) The highlighted cell above shows 2 calculated using our original equation. To find , we just take the square root, so = 1.966 d) j 2 for each j is given in the spreadsheet above. e) From our spreadsheet calculation, <j 2 > = 466.115 f) To find 2 using the equation we derived in problem 1, we just take j 2 - j 2 = 466.115 21.5 2 = 466.115 462.25 = 3.865 = 2 , so = 1.966 and the two methods agree as expected....
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This note was uploaded on 04/17/2008 for the course PHYS 4120 taught by Professor Vajk during the Spring '08 term at Missouri (Mizzou).

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HW1 solutions - Physics 4120 Spring 2008 Homework #1...

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