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On the Sturm-Liouville problem for the complex cubic oscillator. (English) Zbl 1076.34026

The author considers the Sturm-Liouville problem associated with a one-parameter family of non-Hermitian Hamiltonians. By an exact asymptotic method, he gives some results on the eigenvalues and also on the distribution of zeros of eigenfunctions.

MSC:

34B24 Sturm-Liouville theory
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
34B40 Boundary value problems on infinite intervals for ordinary differential equations
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