3) (30 pts.) Two spin 1/2 particles are in a box. The first particle is an...

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3) (30 pts.) Two spin 1/2 particles are in a box. The first particle is an electron while the second particle has no charge, and therefore no magnetic moment. The box is inside a magnetic field of magnitude B in the+z direction. At t = 0, the total spin of the box is measured, and the box is found to be in the Stotal = 0 state. Considering how the presence of the magnetic field affects the time evolution of the spin states of the two particles, what is the earliest time (t > 0) at which a measurement of the total spin of the box will yield Stotal = 1 with 100% probability? (Food for thought: what happened to conservation of angular momentum?) 3) (30 pts.) Two spin 1/2 particles are in a box. The first particle is an electron while the second particle has no charge, and therefore no magnetic moment. The box is inside a magnetic field of magnitude B in the+z direction. At t = 0, the total spin of the box is measured, and the box is found to be in the Stotal = 0 state. Considering how the presence of the magnetic field affects the time evolution of the spin states of the two particles, what is the earliest time (t > 0) at which a measurement of the total spin of the box will yield Stotal = 1 with 100% probability? (Food for thought: what happened to conservation of angular momentum?)