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news_041511 - a n the state vector becomes the...

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Stuff for Friday, April 15, 2011 Stop at 4pm today for Quiz 3 on Q5/Q6 Formulas for today’s quiz: v = λ f k = 2 π λ ω = 2 π f λ = h p λ = hc p 2 ( mc 2 ) K E = hf = hc λ K = hf - W cos θ = 1 2 ` e i θ + e - i θ ´ i sin θ = 1 2 ` e i θ - e - i θ ´ | + x i = » p 1 / 2 p 1 / 2 , | + y i = » p 1 / 2 i p 1 / 2 , | + z i = » 1 0 |- x i = » p 1 / 2 - p 1 / 2 , |- y i = » i p 1 / 2 p 1 / 2 , |- z i = » 0 1 Erratum for Q5S.3 (thanks to Nicholas Jarjour): For the special case of θ = 180 , there will be no output from the positive outlet of the SG θ device. Q6 loose ends eigenvectors of position probability calculations with wave functions two-slit interference
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Six Rules that Quantons Live By 1 State vector | ψ i describes quanton state. Normalized: h ψ | ψ i = 1. | ψ i = ψ 1 ψ 2 . . . h ψ | = ψ * 1 ψ * 2 . . . h ψ | ψ i = ψ * 1 ψ * 2 . . . ψ 1 ψ 2 . . . = | ψ 1 | 2 + | ψ 2 | 2 + · · · = 1 2 For each outcome (value), there is an eigenvalue and an eigenvector. E.g., S x value + s (eigenvalue) has | + x i = » p 1 / 2 p 1 / 2 (eigenvector) 3 When an experiment determines an outcome
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Unformatted text preview: a n , the state vector becomes the corresponding eigenvector A n . “Collapse!” 4 If | ψ i is the initial state, the probability that a measurement collapses it to A n with value a n is: P ( a n ) = |h ψ | A n i| 2 where | ( a + bi ) | 2 = a 2 + b 2 5 Superposition: | ψ i = c 1 | + y i + c 2 |-y i = | + y ih + y | ψ i + |-y ih-y | ψ i (Be able to derive 2nd equality.) The c i ’s are not the eigenvalues!!! 6 Any | ψ i can be decomposed into energy eigenvectors (they “span” the space): | ψ ( t = ) i = c 1 | E 1 i + c 2 | E 2 i + ··· At time t : | ψ ( t ) i = c 1 e-iE 1 t / ~ | E 1 i + c 2 e-iE 2 t / ~ | E 2 i + ··· ( ~ ≡ h / 2 π )...
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