An electron spin sits in a weak magnetic field whose magnitude corresponds to a…

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Quantum dynamics and its formulations · Quantum dynamics and its formulations

The Structure of Quantum Mechanics, Ch Slow change, sudden change and the Berry phase

Problem

An electron spin sits in a weak magnetic field whose magnitude corresponds to a Larmor frequency

f_L = 10\,\mathrm{MHz}

. A pulsed coil reverses the field direction (a rotation of the field axis by

\pi

) in a time

T = 1.0\,\mathrm{ns}

.The level spacing between the two instantaneous spin eigenstates along the field is

\hbar\omega_L

with

\omega_L = 2\pi f_L

. Take the rate at which the eigenstates rotate to be

|\dot\beta| \sim \pi/T

, the average angular rate of the field's rotation. ((a)) Compute

\omega_L

and

|\dot\beta|

. ((b)) Decide whether the field reversal is adiabatic or sudden, quoting the ratio

|\dot\beta|/\omega_L