I need some help with this quantum mechanics question. Figure 3.9(b) is in the second image. It might also be helpful for you to draw the spatial coordinate system. Two Physics 471 students want to have some fun. They set up an experiment similar to the onein the previous problem: as before, the first Stern-Gerlach analyzer allows only particles withspin up along the z-axis to pass through, but this time the second Stern-Gerlach analyzer allowsonly particles with spin up along the x-axis to pass through. The analyzers are separated by aregion of space where there is a uniform magnetic field Bo. The students are free to choose thedirection of Bo, but they want to arrange it so that 100% of the silver atoms that were transmittedby the first analyzer are also transmitted by the second analyzer.Student A finished the two previous problems and says that they should orient the magnetic fieldBo along the +ŷ direction so she can use her results from those problems.Student B looked at Figure 3.9(b) in McIntyre and thought it would be cool to orient the field Boin the x-z plane at an angle of 45° with respect to the z-axis. (In spherical coordinates, Bo wouldbe pointing in the n direction given by 0 = π/4 and =0.)a) If they follow student A's suggestion, what is the minimum time the particles must spendin the magnetic field so that 100% of the particles transmitted by the initial z-analyzer aretransmitted by the final x-analyzer? Define wo = Bo and express your answer in terms of 000.mHint: Although the field is oriented along +y axis rather than the +x axis as in problems 1 and 2,the physics is the same, so the results should be the same.b) If they follow student B's suggestion, what is the minimum time the particles must spendin the magnetic field so that 100% of the particles transmitted by the initial z-analyzer aretransmitted by the final x-analyzer? Hint: You may be tempted to use Equation (3.48), butthat's not necessary. Take seriously the claim that "expectation values in quantum mechanicsobey the laws of classical mechanics" and think about how the direction of the spin vector variesin time. McIntyre's Figure 3.9(b) should be helpful.c) If they follow student A's suggestion and do the calculations correctly, but theyaccidentally orient the B-field along the -ŷ direction instead of the + direction, what fraction ofthe particles transmitted by the initial z-analyzer will be transmitted by the final x-analyzer?Could they get that fraction back to 100% by changing the time that the particles spend in themagnetic field?d) If they follow student B's suggestion but they accidentally orient the B-field in theopposite direction, what fraction of the particles transmitted by the initial z-analyzer will betransmitted by the final x-analyzer? (a)P+→→1.00.80.60.40.202Two4T@o6Two(b)ZA(S(0))B(S(t))yXFIGURE 3.9 (a) Spin-flip probability for a uniform magnetic field with x- and z-components and(b) the corresponding precession of the expectation value of the spin.

Question

I need some help with this quantum mechanics question. Figure 3.9(b) is in the second image. It might also be helpful for you to draw the spatial coordinate system. Two Physics 471 students want to have some fun. They set up an experiment similar to the onein the previous problem: as before, the first Stern-Gerlach analyzer allows only particles withspin up along the z-axis to pass through, but this time the second Stern-Gerlach analyzer allowsonly particles with spin up along the x-axis to pass through. The analyzers are separated by aregion of space where there is a uniform magnetic field Bo. The students are free to choose thedirection of Bo, but they want to arrange it so that 100% of the silver atoms that were transmittedby the first analyzer are also transmitted by the second analyzer.Student A finished the two previous problems and says that they should orient the magnetic fieldBo along the +ŷ direction so she can use her results from those problems.Student B looked at Figure 3.9(b) in McIntyre and thought it would be cool to orient the field Boin the x-z plane at an angle of 45° with respect to the z-axis. (In spherical coordinates, Bo wouldbe pointing in the n direction given by 0 = π/4 and =0.)a) If they follow student A's suggestion, what is the minimum time the particles must spendin the magnetic field so that 100% of the particles transmitted by the initial z-analyzer aretransmitted by the final x-analyzer? Define wo = Bo and express your answer in terms of 000.mHint: Although the field is oriented along +y axis rather than the +x axis as in problems 1 and 2,the physics is the same, so the results should be the same.b) If they follow student B's suggestion, what is the minimum time the particles must spendin the magnetic field so that 100% of the particles transmitted by the initial z-analyzer aretransmitted by the final x-analyzer? Hint: You may be tempted to use Equation (3.48), butthat's not necessary. Take seriously the claim that &#34;expectation values in quantum mechanicsobey the laws of classical mechanics&#34; and think about how the direction of the spin vector variesin time. McIntyre's Figure 3.9(b) should be helpful.c) If they follow student A's suggestion and do the calculations correctly, but theyaccidentally orient the B-field along the -ŷ direction instead of the + direction, what fraction ofthe particles transmitted by the initial z-analyzer will be transmitted by the final x-analyzer?Could they get that fraction back to 100% by changing the time that the particles spend in themagnetic field?d) If they follow student B's suggestion but they accidentally orient the B-field in theopposite direction, what fraction of the particles transmitted by the initial z-analyzer will betransmitted by the final x-analyzer? (a)P+→→1.00.80.60.40.202Two4T@o6Two(b)ZA(S(0))B(S(t))yXFIGURE 3.9 (a) Spin-flip probability for a uniform magnetic field with x- and z-components and(b) the corresponding precession of the expectation value of the spin.

Accepted Answer

Answered: Image /qna-images/answer/db5c3691-ece1-4bca-8135-24874ea2be0e.jpg