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Spin Precession Consider a spin-1/2 system with a magnetic moment µ = -e/ms which starts in the |+) state, i.e. J(t = 0)) = |+). (a) If the observable S, is measured at time t = 0, what are the possible measure- ment results and probabilities for those results? (b) Now consider the case where we do not measure Š, initially. Instead, the system is allowed to evolve in a uniform magnetic field along the à direction, ie. B= Boî. Calculate the state of the system |v(t)) after a time t has passed. (c) Supposed the observable Š, is measured at time t. What is the probability that you will measure spin-down in the y direction (i.e. -h/2?) Sketch the probability P-y as a function of time. Check that your t = part (a)! O results match

Spin Precession Consider a spin-1/2 system with a magnetic moment µ = -e/ms which starts in the |+) state, i.e. J(t = 0)) = |+). (a) If the observable S, is measured at time t = 0, what are the possible measure- ment results and probabilities for those results? (b) Now consider the case where we do not measure Š, initially. Instead, the system is allowed to evolve in a uniform magnetic field along the à direction, ie. B= Boî. Calculate the state of the system |v(t)) after a time t has passed. (c) Supposed the observable Š, is measured at time t. What is the probability that you will measure spin-down in the y direction (i.e. -h/2?) Sketch the probability P-y as a function of time. Check that your t = part (a)! O results match

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Spin Precession Consider a spin-1/2 system with a magnetic moment µ = -e/mS which starts in the |+) state, i.e. J(t = 0)) = |+). (a) If the observable Š, is measured at time t = 0, what are the possible measure- ment results and probabilities for those results? (b) Now consider the case where we do not measure Š, initially. Instead, the system is allowed to evolve in a uniform magnetic field along the î direction, ie. B= B,î. Calculate the state of the system |v(t)) after a time t has passed. (c) Supposed the observable Š, is measured at time t. What is the probability that you will measure spin-down in the y direction (i.e. -h/2?) Sketch the probability P-y as a function of time. Check that your t = part (a)! O results match
Transcribed Image Text:Spin Precession Consider a spin-1/2 system with a magnetic moment µ = -e/mS which starts in the |+) state, i.e. J(t = 0)) = |+). (a) If the observable Š, is measured at time t = 0, what are the possible measure- ment results and probabilities for those results? (b) Now consider the case where we do not measure Š, initially. Instead, the system is allowed to evolve in a uniform magnetic field along the î direction, ie. B= B,î. Calculate the state of the system |v(t)) after a time t has passed. (c) Supposed the observable Š, is measured at time t. What is the probability that you will measure spin-down in the y direction (i.e. -h/2?) Sketch the probability P-y as a function of time. Check that your t = part (a)! O results match
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