A beam of neutrons with spins along the positive z-axis suddenly enters a region where there is a uniform magnetic field B = 1.5 T (Tesla) in the positive x-direction. Ignoring the spatial degrees of freedom (a) find the spin state of the system at any time t after entering the B field region and interpret what is happening. Hint: Use the Euler relation and corresponding Taylor expansions
A beam of neutrons with spins along the positive z-axis suddenly enters a region where there is a uniform magnetic field B = 1.5 T (Tesla) in the positive x-direction. Ignoring the spatial degrees of freedom (a) find the spin state of the system at any time t after entering the B field region and interpret what is happening. Hint: Use the Euler relation and corresponding Taylor expansions
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Transcribed Image Text:A beam of neutrons with spins along the positive z-axis suddenly enters a region where there is
a uniform magnetic field B = 1.5 T (Tesla) in the positive x-direction. Ignoring the spatial
degrees of freedom
(a) find the spin state of the system at any time t after entering the B field region and interpret
what is happening. Hint: Use the Euler relation and corresponding Taylor expansions
exp (iA) = cos A + i sin A
Σ (iA)/n!
n=0
=
∞
Σ (iA)"/n! + Σ (iA)" /n!
n = odd
n = even
(b) What is the earliest time t that the system has evolved to have the spin completely flipped,
so it is definitely along the negative z-direction? (Look up the gyromagnetic ratio for the
neutron).
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