An electron is subject to a uniform, time-independent, magnetic field of strength B in the z-directionAt t 0 an electron is prepared in anlying in the rz-plane, that makes aneigenstate of S n with eigenvalue h/2, wheren is a unit vectorangle B with the z-axis.(a) What is the probability of finding the electron spin in the Sa = h/2 state as a function of time?(b) Find (Sa)as a function of time(c) Check the limitingcases as discussed in class to confirm your answers.

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Asked Oct 9, 2019
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It's a quantum mechanics question.

An electron is subject to a uniform, time-independent, magnetic field of strength B in the z-direction
At t 0 an electron is prepared in an
lying in the rz-plane, that makes an
eigenstate of S n with eigenvalue h/2, wheren is a unit vector
angle B with the z-axis.
(a) What is the probability of finding the electron spin in the Sa = h/2 state as a function of time?
(b) Find (Sa)
as a function of time
(c) Check the limiting
cases as discussed in class to confirm your answers.
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An electron is subject to a uniform, time-independent, magnetic field of strength B in the z-direction At t 0 an electron is prepared in an lying in the rz-plane, that makes an eigenstate of S n with eigenvalue h/2, wheren is a unit vector angle B with the z-axis. (a) What is the probability of finding the electron spin in the Sa = h/2 state as a function of time? (b) Find (Sa) as a function of time (c) Check the limiting cases as discussed in class to confirm your answers.

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Step 1

The unit vector n and the spin vector S can be represented in the xz plane as,

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sin 0x cos 0z n h S -G 2 h (x+y) 2

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Step 2

In the second equation above σ is the representation of the pauli spin vector and θ is the angle between the direction of the Spin angular momentum vector S and the z axis.

Hence the dot product of the spin angular momentum S vector and the unit vector n can be represented as,

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h (sin00,+cos0o,) 2 Sn=

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Step 3

Let |ψ> denote an eigenstate of the operat...

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S)) S.n 2

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