- #1
- 753
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Homework Statement
What kind of conditions do eigenvalues impose to ensure periodicity?
Is it plausible to say that irrational multiples of eigenvalues imply no harmonic oscillations, if so why?
[tex]
\left[\begin{array}{cccc}0 & -a & 0 & 0 \\ -a & 0 & -b & 0 \\ 0 & -b & 0 & -c \\ 0 & 0 & -c & 0\end{array}\right]
[/tex]
For any fixed a, I want to find b and c in terms of a such that lambda_i / lambda_ j is a rational number for every i,j=1,2,3,4 .
See, before I was working with
[tex]
\left[\begin{array}{cccc}0 & -a & 0 & 0 \\ -a & 0 & -a & 0 \\ 0 & -a & 0 & -a \\ 0 & 0 & -a & 0\end{array}\right]
[/tex]
But that gave me irrational e-values if I put it into Maple and I don't want that.