Consider an arrangement of three consecutive Stern-Gerlach (SG) apparatus oriented along , n, and z. The...

 

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Consider an arrangement of three consecutive Stern-Gerlach (SG) apparatus oriented along ż, n, and z. The vector n is in the xz-plane and, as a result, its polar coordinates are (0,0). A beam of silver atoms is directed into the first SG-apparatus. The-h/2 spins (spins down) are then stopped. The ħ/2 spins (spins up) continue along their path and pass through the second SG-apparatus. Only the h/2 spins (spins up) are then allowed to pass through the third SG-apparatus. A sketch of this arrangements is presented in the figure below. Compute the fractions of silver atom atoms that come out from the third SG-apparatus with (i) spin up, (ii) spin down, and (iii) the fraction that never reaches the end of the path. Show what happens for 0 = 0 ( along the z-direction) and for 0 = π/2 (ñ along the x-direction). SG z-direction h/2 -h/2 SG n-direction h/2 -h/2 SG z-direction h/2 -h/2 Consider an arrangement of three consecutive Stern-Gerlach (SG) apparatus oriented along ż, n, and z. The vector n is in the xz-plane and, as a result, its polar coordinates are (0,0). A beam of silver atoms is directed into the first SG-apparatus. The-h/2 spins (spins down) are then stopped. The ħ/2 spins (spins up) continue along their path and pass through the second SG-apparatus. Only the h/2 spins (spins up) are then allowed to pass through the third SG-apparatus. A sketch of this arrangements is presented in the figure below. Compute the fractions of silver atom atoms that come out from the third SG-apparatus with (i) spin up, (ii) spin down, and (iii) the fraction that never reaches the end of the path. Show what happens for 0 = 0 ( along the z-direction) and for 0 = π/2 (ñ along the x-direction). SG z-direction h/2 -h/2 SG n-direction h/2 -h/2 SG z-direction h/2 -h/2 Consider an arrangement of three consecutive Stern-Gerlach (SG) apparatus oriented along ż, n, and z. The vector n is in the xz-plane and, as a result, its polar coordinates are (0,0). A beam of silver atoms is directed into the first SG-apparatus. The-h/2 spins (spins down) are then stopped. The ħ/2 spins (spins up) continue along their path and pass through the second SG-apparatus. Only the h/2 spins (spins up) are then allowed to pass through the third SG-apparatus. A sketch of this arrangements is presented in the figure below. Compute the fractions of silver atom atoms that come out from the third SG-apparatus with (i) spin up, (ii) spin down, and (iii) the fraction that never reaches the end of the path. Show what happens for 0 = 0 ( along the z-direction) and for 0 = π/2 (ñ along the x-direction). SG z-direction h/2 -h/2 SG n-direction h/2 -h/2 SG z-direction h/2 -h/2 Consider an arrangement of three consecutive Stern-Gerlach (SG) apparatus oriented along ż, n, and z. The vector n is in the xz-plane and, as a result, its polar coordinates are (0,0). A beam of silver atoms is directed into the first SG-apparatus. The-h/2 spins (spins down) are then stopped. The ħ/2 spins (spins up) continue along their path and pass through the second SG-apparatus. Only the h/2 spins (spins up) are then allowed to pass through the third SG-apparatus. A sketch of this arrangements is presented in the figure below. Compute the fractions of silver atom atoms that come out from the third SG-apparatus with (i) spin up, (ii) spin down, and (iii) the fraction that never reaches the end of the path. Show what happens for 0 = 0 ( along the z-direction) and for 0 = π/2 (ñ along the x-direction). SG z-direction h/2 -h/2 SG n-direction h/2 -h/2 SG z-direction h/2 -h/2