Unformatted text preview: Quantum Mechanics: Give up the idea of predicting the result of a single measurement! Can determine only the probability of each of the many possible outcomes. Knowing the probabilities allows one to calculate average quantities and standard deviations. Rolling the Dice: It is like rolling a dice. You know there is a one in six chance of rolling a one, so that if you roll the dice millions of times then, on the average, the value one will occur 1/6 of the time. However, on a given roll you do not know which of the six numbers will appear. Gauge Invariance: Note that the following two wave functions describe the same state: ) , ( ) , ( 1 t r t r r r Ψ = Ψ and ) , ( ) , ( 2 t r e t r i r r Ψ = Ψ φ . Wave Packet321 1 2 3 x v group At fixed time t Probability amplitude! Many amplitudes correspond to the same probability! Also require Ψ to be continuous and singlevalued!...
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 Spring '07
 Field
 Physics, Probability, probability density, ψn, Probability amplitude, R. D. Field

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