c120a_lecture2

# c120a_lecture2 - Chem 120A Probability Theory and...

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Unformatted text preview: Chem 120A Probability Theory and Double-Slit Experiments 01/19/06 Spring 2007 Lecture 2 READING: Read Feynmann Lectures in Physics, vol III: Chapter 1(on the web) Two rules for probabilities Recall the experimental setup from the last lecture: x y Source Detector Figure 1: An experiment for considering probability. Particles are emitted from the source S with random velocities. The particles then strike the detector at some point along y . The detector counts the number of strikes at each point. The probability of a particle striking at a point y is P ( y ) = lim N N ( y ) N , (1) where N ( y ) is the number of particles hitting the point y and N is the total number of particles emitted from the source. The total probability of finding a particle at either a point, y 1 , or another point y 2 as P ( y 1 , y 2 )= P ( y 1 )+ P ( y 2 ) . Rule 1 : For mutually exclusive events, probabilities add . Suppose particles from the source S can hit a detector only at discrete points y 1 , y 2 , . . . , y N . Then the total probability of finding a particle anywhere on the detector is P ( { y } ) = N i = 1 P ( y i ) = 1 . In real life, often events are defined on continuos intervals. For example, particles from the source S can hit Chem 120A, Spring 2007, Lecture 2 1 the detector anywhere, not just at points y 1 or y 2 . We treat such situations a little bit differently. Suppose we assign a length, , to each region along the detector: x y Source Detector } Figure 2: Each point along the detector is now associated with a length . We effectively devide the detector ( y-axis in this case) into disjoint intervals i . We define probability per unit length in an interval i . Bin y i collects/counts all particles that hit interval i . Let i = for all i ....
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## c120a_lecture2 - Chem 120A Probability Theory and...

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