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Lecture_09 - PHYS 342 Fall 2010 Lecture Lecture 09...

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PHYS 342 Fall 2010 Lecture 09: Expectation Values, Operators Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 09 1
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Measuring the position of an oscillating mass No. of occurrences Measured value spring n 1 x 1 n 2 x 2 n 3 x 3 +Force constant k(N/m) . . . . x=0 n m x m x 0 x final What is the average value of x? U(x) E 1 1 ; i i N N i i i i n x n x x N n K.E. 1 i N i i N n 0 x o x o 2
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When we do not have a predictable outcome for a measurement, we must deal with probability densities and/or probability distributions Consider some The probability distribution with probability densities and/or probability distributions. Consider some quantity that varies continuously, for example the height of a Purdue student. We could coerce a group of students to report their height and we could make a plot of height in 10-cm intervals as shown below. Nobody will be exactly 180 cm or 190 cm tall, so we just group students into height intervals and systematically round things up at the edges of each bin. If we want finer detail, we could group heights in 1-cm intervals or 1-mm intervals, which will continue to make things discrete. But as the intervals b ll th hi t bl ti Thi i 3 become smaller, the histogram resembles a continuous curve. This curve is known as the probability distribution . http://theochemlab.asu.edu/teaching/phy571/supp02.pdf
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