Chapter1_9 - Let Ψ 1 be the amplitude for an electron to...

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PHY4604 R. D. Field Department of Physics Chapter1_9.doc University of Florida General Principles: Probability Amplitudes I. The probability of an event is given by the square of the absolute value of a complex number Ψ , which is called the “probability amplitude” : P = probability Ψ = “wave function” = “probability amplitude” P = | Ψ | 2 II. When an event can occur in several alternative ways, the probability amplitude is the sum of the probability amplitudes for each way considered separately: Ψ = Ψ 1 + Ψ 2 P = | Ψ 1 + Ψ 2 | 2 = P 1 + P 2 +2Re( Ψ 1 Ψ 2 * ) P 1 + P 2 III . If an experiment is performed which is capable of determining whether one or the other alternative is actually taken, then the probability of the event is the sum of the probabilities for each alternative: P = P 1 + P 2 Example: Double Slit Experiment
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Unformatted text preview: Let Ψ 1 be the amplitude for an electron to go from the source S through slit 1 and arrive at the point P on the screen. Let Ψ 2 be the amplitude for an electron to go from the source S through slit 2 and arrive at the point P on the screen. If no experiment is done to determine which hole the electron went through then the probability of finding the electron at the point P on the screen is P = | Ψ 1 + Ψ 2 | 2 = P 1 + P 2 +2Re( Ψ 1 Ψ 2 * ) ≠ P 1 + P 2 and “interference” occurs. If an experiment is performed to determine which hole the electron went through then the probability of finding the electron at the point P on the screen is P = P 1 + P 2 = | Ψ 1 | 2 + | Ψ 2 | 2 . Interference! No interference! 1 P Screen Ψ 1 Source Double Slit 2 Ψ 2...
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This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.

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