Sturm-Liouville Problem

Find the n-th eigen-value λ and the corresponding eigen-function u:[α,β]→R of the Sturm-Liouville problem:

-u''(x)+drift(x)u'(x)+potential(x)u(x)=λu(x)

subjected to: h₁u(α)+k₁u'(α)=0 and h₂u(β)+k₂u'(β)=0.
Or find the n-th eigen-value λ and the corresponding eigen-function of the 4-th order problem:

u''''(x)+drift(x)u'(x)+potential(x)u(x)=λu(x)

subjected to: u(α)=u'(α)=u(β)=u'(β)=0.
In any case α and β denote the left and the right end point of the interval, respectively.

Please use standard C notation for math especially x for the variable. Any other notation will produce an unknown variable error!

Interval end points, boundary conditions, eigen-function number n, minimal eigen-value and order.

Exit

Gnuplot graphics! Eigen-function and corresponding Eigen-value
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Potential

Density of invariant probability