Example: Calculating probabilities for measuring spin-up and spin-down

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Example calculation for the probabilities of both spin-up and spin-down, including the check that the add to 1.
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In the real world, do you ever know what quantum state a system is in (the 2 and 3i in your problem)? If so, how are they discovered? If not, why would it matter that you can use the state to calculate probabilities?

stephenrothman
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At 03:23 you say "1" but you write "0". Is this quantum uncertainty? :-)

dirklutz