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Introductory Physics Homework Help
Determine the number of particles transmitted by S-G analyzer
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[QUOTE="acdurbin953, post: 5379630, member: 538058"] Thank for the insight that the direction does not affect the Hamiltonian - I hadn't realized that. Starting from the beginning, I let my prepared state be |ψ(0)> = |+>. This enters the B-field and since the probability is dependent on time, I need to apply U = e[SUP]iωt/2[/SUP] to my time evolved state |ψ(t)>. If I catch you drift, I should write |ψ(0)> in the x basis at this point? So |ψ(0)> = 1/√2 (|+> + |->). Then the time evolved state passing through the B-field before it enters the second analyzer is |ψ(t)> = 1/√2 * (e[SUP]-iωt/2[/SUP] |+> + e[SUP]iωt/2[/SUP] |->) The probability I am looking for with this state coming from the second analyzer is then |<-|ψ(t)>|[SUP]2[/SUP]. Next I applied Euler's, and the probability becomes P[SUB]-[/SUB] = 1/2 |cos(ωt/2) + isin(ωt/2)|[SUP]2[/SUP] = 1/4 Is that looking correct? I am not sure what to do about all of the cos and sin terms I end up with when I square what is inside the abs value. It doesn't seem there is a clean way to extract t. Should I not use Euler's? [/QUOTE]
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Introductory Physics Homework Help
Determine the number of particles transmitted by S-G analyzer
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