Re: how to define spin polarization? thank you

hygrogen <[EMAIL PROTECTED]> wrote:
> what is its exact defination? It is the ratio of the up number to the
> down number of electron spin ?

i've seen the polarization (of an ensemble) defined as the total-spin 
expectation value: \vec{I} = \sum_k \vec{I}^{(k)}, P = sqrt{<\vec{I}^2>}
to get a percentage one would divide by the maximum possible number, 
i.e., n*j for a system of n spin-j objects.

the number of spins pointing up or down may not be well-defined if there 
are correlations between individual spins.
But if you are thinking of an ensemble of independent electrons then
you can define the z-direction such that |up>,|down>  correspond to the 
eigenvectors of rho and 
  
polarization = (number of spins up)/(total number of electrons)

> in what conditons, the spin will polarize? except external magnetic
> field, why hydrogen atoms would polarize?

there are other ways to achieve polarization
for example optical pumping, spin-spin interaction in a ferromagnetic 
system, or interaction with another polarized system.

hth
 Geza

-- 
 Geza Giedke, Wehntalerstrasse 309, CH-8046 Zuerich

 Institut fuer Quantenelektronik, ETH Zuerich