Revisit the 2 Spins

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What is $\rho(z)$ ?

$\begin{displaymath} \rho(x) = \mbox{\raisebox{-.5ex}{$s_{0} [\delta(z+z_{0}) + \delta(z-z_{0})]$}} \end{displaymath}$ (9.17)
Take Fourier transform of $\rho(x)$ with a constant gradient on. Does it give the beating we expect ???

$\displaystyle s(t)$ $\textstyle =$ $\displaystyle s_{0} e^{-i\gamma G z_{0} t} + s_{0} e^{i \gamma G z_{0}t}$

$\textstyle =$ $\displaystyle 2 s_{0} \cos {(\gamma G t z_{0})} \hspace{0.5in} 0<t<t_2$ (9.18)
Only see a cosine, but we have taken out the Larmor frequency via demodulation. If we had not done this, would have a beating signal.

Next: What about a distribution Up: Couple of Important Mathematical Previous: Couple of Important Mathematical Contents

Michael Thompson 2003-11-21

$\displaystyle s(t)$	$\textstyle =$	$\displaystyle s_{0} e^{-i\gamma G z_{0} t} + s_{0} e^{i \gamma G z_{0}t}$
	$\textstyle =$	$\displaystyle 2 s_{0} \cos {(\gamma G t z_{0})} \hspace{0.5in} 0<t<t_2$	(9.18)