On Eigenvalues of the Schrodinger Operator with an Even Complex-Valued Polynomial Potential
2012 (English)In: Computational methods in Function Theory, ISSN 1617-9447, Vol. 12, no 2, 465-481 p.Article in journal (Refereed) Published
In this paper, we generalize several results in the article Analytic continuation of eigenvalues of a quartic oscillator of A. Eremenko and A. Gabrielov . We consider a family of eigenvalue problems for a Schrodinger equation with even polynomial potentials of arbitrary degree d with complex coefficients, and k < (d + 2)/2 boundary conditions. We show that the spectral determinant in this case consists of two components, containing even and odd eigenvalues respectively. In the case with k = (d + 2)/2 boundary conditions, we show that the corresponding parameter space consists of infinitely many connected components.
Place, publisher, year, edition, pages
2012. Vol. 12, no 2, 465-481 p.
Nevanlinna functions, Schrodinger operator
IdentifiersURN: urn:nbn:se:su:diva-88370ISI: 000313424300007OAI: oai:DiVA.org:su-88370DiVA: diva2:611248