c120a_lecture2 - Chem 120A Probability Theory and...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

Page1 / 5

c120a_lecture2 - Chem 120A Probability Theory and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online