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Re: [Phys-l] question about coupled oscillators



The argument is erroneous. The reality condition is on the eigenvalues, not the eigenvectors.
Jack


On Sat, 4 Nov 2006, Carl Mungan wrote:

Having thought about it a little more, this is what I come up with:

Newton's third law says that oscillators i and j exert equal
magnitude forces on each other. This in turn will lead to elements
K_ij and K_ji in the force-constant matrix K to be equal. In turn,
this means K is symmetric (and of course it's real); and so is the
mass matrix M. But this means the eigenvectors must be real, even if
I write the oscillator displacement vector x in complex form where
the i-th component is A_i exp (i d_i). But this means d_i can only be
0 or pi.

What do you think of this argument? -Carl


--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley