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View Full Version : Coupled Harmonic Oscillator or coupled Sturm-Liouville problem


Wattok
Aug2-11, 09:27 PM
I would like to know if someone of you has references about the following system of equations (related to a coupled system of harmonic oscillators or coupled Sturm-Liouville problem):

[\partial_{xx}-(q(x)^2 + q(x)' \sigma_1)]X(x) = \lambda^2 X(x)

where

X(x):=\big((u(x), v(x)\big)^T
\sigma_1 is the Pauli matrix: http://en.wikipedia.org/wiki/Pauli_matrices
\lambda is a constant.

Thank you in advance!