hw7 - Assignment #7 PHYS-446 due in class on 21 November...

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Assignment #7 PHYS-446 due in class on 21 November 2008 1. Prove Schwarz Inequality: ∣⟨ a b ⟩∣  ∣ a ∣ ∣ b To do this, consider the axiom c c ⟩  0 , applied to c = a b a b 2 b 2. (Griffiths, Problem 3.27) An operator A , representing observable A , has two normalized eigenstates 1 and 2 , with eigenvalues a 1 and a 2 , respectively. Operator B , representing observable B , has two normalized eigenstates 1 and 2 , with eigenvalues b 1 and b 2 . The eigenstates are related by 1 = 3 1 4 2 / 5, 2 = 4 1 3 2 / 5 (a) Observable A is measured, and the value a 1 is obtained. What is the state of the system (immediately) after this measurement? (b) If B is now measured, what are the possible results, and what are their probabilities? (c) Right after the measurement of B , A is measured again. What is the total probability of getting back a value
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hw7 - Assignment #7 PHYS-446 due in class on 21 November...

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