Lecture3-4Notes

Lecture3-4Notes - R A Harris The Two Slit Experiment 1 The...

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R. A. Harris The Two Slit Experiment 1 The best introduction to the structure of quantum mechanics is an analysis of the two slit experiment 'a la' Feynm'v Volume III. We will follow Feynman's development quite closely, but we shall embellish at . - various p;j'ints. The beauty Qf the two slit experiment is that so many physical points can be made without quantitative mathematical analysis. The two slit experiment will be used in tbree configurations and in three situations. . I R z Configurations: I) Only hole 'a' open (a) Only hole 'b' open (b) III) Both holes open (ab) We first consider classical particles. There are two equivalent ways (by equivalent, we mean that the results will be the same after a sufficiently long set of runs are performed) of looking at this set of experiments: 1) Particles are slowly emitted from a source and are counted at points along y. There are no interactions amongst the particles. 2) There is only ONE particle and it is recycled from the detector back to the source. In all cases, we count the fraction (or frequency) of particles arriving at a point y. For the time being, we assume that we measure the fraction in a region. Then we define a probability as P(Y) = ,,ZN(~)/N. N(y) is the number which end up at y, and is divided by N, the total number of times the experiment is carried out (i.e. the number of times a particle is emitted from S.) For the three configurations, we have Pa(y), Pb(y) and Pab(y). Since the particle cannot go through both holes simultaneously, we must have Pab(y) = Pa(y) + Pb(y). M.O,E*: There is a third way of looking -. at this experiment. Suppose we set up an infinite number of identical apparatuses and carry out each
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experiment once. This way of looking at probability is called the 'ensemble' way. We would have P,"(y), P<(y), and Pa<(y). P,"(y) represents the fraction of apparatuses which end up with the particle at y. It is generally assumed that in the limit, P(y) = P(y) for all cases. As we shall see, when we study quantum information theory, it is very important to be precise about what is meant by probabilities. Secondly, we consider classical waves. In the case of fluids or solids, wave behavior is a derived result coming about from coupled particles. In E&M, it is fundamental- a conceptual leap. I find these waves difficult to fathom- except as they move matter. Getting back to the classical wave case, we measure the intensity at the detector (i.e. the energy crossing unit area per unit time), I(y). In this case, we find that Iab(y) ;t Ia(y) + Ib(y). There is an oscillatory behavior in Iab(y) which was not present in Pab(y). Wave theory has deduced that one can describe waves by amplitudes. Even though one can actually measure amplitudes, it is convenient to introduce complex numbers: Aa(y), Ab(y) and.A.ab(y),
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This note was uploaded on 09/29/2009 for the course CHEM 120A taught by Professor Whaley during the Spring '07 term at Berkeley.

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Lecture3-4Notes - R A Harris The Two Slit Experiment 1 The...

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