Cyclic Sturm-Liouville Problem

Find the n-th eigen-value λ and the corresponding eigen-function(s) u:[-1,1]→R of the cyclic Sturm-Liouville problem:

-u''(x)+drift(x)u'(x)+potential(x)u(x)=λu(x)
where cyclic means: u(1)=u(-1) and u'(1)=u'(-1). Unlike the standard boundary value case the periodic problem typically appears to have eigen-values of multiplicity two - apart from the first of course. Thus in most cases the graph of two functions will be displayed.
Please use standard C notation for math and especially x for the variable. Any other notation will produce an unknown variable error! The potential may exhibit singularities!

Eigen-function number. Accuracy of multiplicities is not that reliable. Also, if you think some eigen-values have been omitted increase the threshold! Decreasing the threshold (or error) increases accuracy but it may miss an eigen-value or it may exclude a second eigen-function!

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Gnuplot graphics! Eigen-function(s) and corresponding Eigen-value
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Potential

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