Lecture_18

Lecture_18 - PHYS 342 all 2011 Fall 2011 Lecture 18:...

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Unformatted text preview: PHYS 342 all 2011 Fall 2011 Lecture 18: Confidence Building Examples: he Hydrogen Atom the Hydrogen Atom e- , m U(r) Lecture 18 1 Probability Density Probability Density 2 * In 1-D, the probability of finding a particle between x and x+dx is * ( ) ( ) x x d x n 3 the probability of finding a Implications for units In 3-D, the probability of finding a particle between (r, , ) and of (r+dr, +d , +d ) is * ( , , ) ( , , ) r r dV 2 The volume element dV in spherical coordinates The paralellpiped approaches a pp rectangular box as dr 0, d 0, d 0, so the volume element just http://www.netcomuk.co.uk/~jenolive/polar.html is just 3 Working it out 2 sin sin dV dr rd r d r dr d d Probability of finding electron at r, , is P(r, , ) : 2 , , , , , , , , , 2 2 ( , , ) ( , , ) ( , , ) ( ) ( , ) ( ) ( , ) ( ) n m n m n m n m m P r r d V r R r Y R r 2 2 2 2 , , , ( , , ) ( ) ( , ) sin ( ) n m m P r r R r dr d d Probability of finding electron between shell of radius r and a shell of radius r+dr: 2 2 2 2 , , , ( ) ( ) ( , ) sin ( ) n m m P r r R r dr d 2 2 2 2 ) ( ) ( ) ( ) ( ) d r r R r dr P r dr if and are normalized , , , , 2 2 ( ) ( ) ( ) ( , ) ( ) n n m m P r r R r dr P r dr if and are normalized Expectation value of some function f(r): 2 , , ( ) ( ) ( ) ( ) ( ) ( ) ( ) n n f r f r P r dr f r r R r...
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Lecture_18 - PHYS 342 all 2011 Fall 2011 Lecture 18:...

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