1. Precession of a rotated spin At time t = 0, the state of an electron spin is l(t = 0)) = | +),n with e = and o The system is allowed to time-evolve in a uniform magnetic field B = B,2. e) Calculate the average values of the three spin operators, , , and as a function of time. (Show your work) Draw a graph for these quantities, and use the graphs to describe in your own words the behavior of the average spin vector . f) What is the expectation value of energy, , as a function of time? Does its time dependence make sense?
1. Precession of a rotated spin At time t = 0, the state of an electron spin is l(t = 0)) = | +),n with e = and o The system is allowed to time-evolve in a uniform magnetic field B = B,2. e) Calculate the average values of the three spin operators, , , and as a function of time. (Show your work) Draw a graph for these quantities, and use the graphs to describe in your own words the behavior of the average spin vector . f) What is the expectation value of energy, , as a function of time? Does its time dependence make sense?
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Transcribed Image Text:1. Precession of a rotated spin
At time t = 0, the state of an electron spin is l(t = 0)) = | +)n with 0 = and o =
The system is allowed to time-evolve in a uniform magnetic field B = Bo2.
e) Calculate the average values of the three spin operators, <Sx>, <Sy>, and <Sz> as a
function of time. (Show your work) Draw a graph for these quantities, and use the
graphs to describe in your own words the behavior of the average spin vector <S>.
f) What is the expectation value of energy, <H>, as a function of time? Does its time
dependence make sense?
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