Re: ? Measuring eigenvalues

jamesahart79_at_gmail.com
Date: 03/11/05 

Date: 11 Mar 2005 08:17:53 -0800

Yes, that's right: Even if the diffusion coefficient changes with
position, the equation is still linear. Green functions still exist,
as do eigenvalues/-functions. They are, however, much harder to find!
Linearity is the key requirement, meaning that if y1 and y2 are each
solutions of the equation, then a*y1+b*y2 is also a solution.

As for determining what kind of equation controls a system---that's
where insight and intuition trump any amount of canned logic any day.
I wish I could just plug my results into a computer and get what kind
of equation it is out, but instead you almost always start with some
mental picture of what might be going on, and work out the results of
that model in detail. You then test to see if your conclusions match
what is going on in the experiment. Very slow, but it's the only way
we've managed to get to work. The view in physics textbooks of
following a predefined path to a set goal works only after the problem
has been around for at least fifty years.

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