Semiclassical approximation for a nonself-adjoint Sturm-Liouville problem with a parabolic potential (Q1048590)

The authors analyze the spectral behavior of the corresponding family of differential operators \(L(\varepsilon )y=i\varepsilon y^{\prime \prime }+q(x)y,\) \(\varepsilon >0\), on the interval \([a,b]\) with the boundary conditions \(y(a)=y(b)\) as \(\varepsilon \rightarrow 0\) for the case in which \(q(x)\) is an analytic function with one extremum on \([a,b]\). For this model problem the authors find the limit spectral graph (the limit curves along which the spectrum is concentrated).