Transforming this into a function for position as a function of time ( relative to some definite laboratory coordinate system ) is nasty and inconvenient-take a look at four-vector for the basics.
2.
Where " N " " s " is the surface number density of the adsorbed molecules, ? and ? are orientational angles relating the molecular coordinate system to the laboratory coordinate system, and represents the average value of x.
3.
For adsorbed molecules in a uniaxial distribution, the only independent hyperpolarizability tensor terms are ? z z z, ? z x x, and ? x x z where terms denote the molecular coordinate system as opposed to the laboratory coordinate system . ? can be related to ? ( 2 ) through orientational averages.
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