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# Time evolution of a spin 1/2 particle in a magnetic field

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##### Solution Summary

A detailed solution for the time evolution of a spin 1/2 particle in a magnetic field is given.

##### Solution Preview

This problem can be solved using the formal solution of the time-dependent Schrödinger equation:

i hbar d|psi>/dt = H|psi> ------->

|psi(t)> = Exp[-i H t/hbar]|psi(0)>

So, let's evaluate the time evolution operator:

Exp[-i H t/hbar] = Exp[-i omega S_x t/hbar]

We know that:

S_x = hbar/2 sigma_x, where sigma_x is the Pauli Matrix [[0,1]
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