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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: 5378570, member: 538058"] [h2]Homework Statement [/h2] A beam of identical neutral particles with spin 1/2 travels along the y-axis. The beam passes through a series of two Stern-Gerlach spin analyzing magnets, each of which is designed to analyze the spin projection along the z-axis. The first Stern-Gerlach analyzer only allows particles with spin up (along the z-axis) to pass through. The second SternGerlach analyzer only allows particles with spin down (along the z-axis) to pass through. The particles travel at speed v[SUB]0[/SUB] between the two analyzers, which are separated by a region of length d in which there is a uniform magnetic field B pointing in the x-direction. Determine the smallest value of d such that only 25% of the particles transmitted by the first analyzer are transmitted by the second analyzer. [h2]Homework Equations[/h2] Rabi's formula: In this instance I said w[SUB]0[/SUB] = 0, so the probability is given by P[SUB]+→-[/SUB] = sin[SUP]2[/SUP](w[SUB]1[/SUB]t/2) [h2]The Attempt at a Solution[/h2] I know that I want 25% of the particles to come out of the second analyzer. Since both analyzers measure along the z-axis, and go from spin-up to spin-down, I have been trying to solve this using Rabi's formula for spin-flip. I set P[SUB]+→-[/SUB] = sin[SUP]2[/SUP](w[SUB]1[/SUB]t/2) = 1/4. However, I am now feeling stuck and I think I have missed some things along the way: 1st: I forgot that the particles are said to be traveling along the y-axis, and I don't know if this matters in the problem. I currently have the input state before the particles enter the B-field as |ψ(0)> = |+>. 2nd: I need to solve for the distance, so I need to find the value of t from solving P[SUB]+→-[/SUB] = 1/4. But I don't know what to use for my value of w[SUB]1[/SUB]. For an electron I see that w = eB/m[SUB]e[/SUB], but I don't know what to use for these neutral particles. [/QUOTE]
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Introductory Physics Homework Help
Determine the number of particles transmitted by S-G analyzer
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