On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential
2012 (English)In: Computational methods and function theory, ISSN 1617-9447, Vol. 12, no 1, 119-144 p.Article in journal (Refereed) Published
We consider the eigenvalue problem with a complex-valued polynomial potentialof arbitrary degree d and show that the spectral determinant of this problem is connected and irreducible. In other words, every eigenvalue can be reached from any other by analytic continuation.We also prove connectedness of the parameter spaces of the potentials that admit eigenfunctions satisfying k>2 boundary conditions, except for the case d is even and k=d/2 In the latter case, connected components of the parameter space are distinguished by the number of zeros of the eigenfunctions.The first results can be derived from H.~Habsch, while the case of a disconnected parameter space is new.
Place, publisher, year, edition, pages
2012. Vol. 12, no 1, 119-144 p.
Nevanlinna functions, Schrödinger operator
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-88598OAI: oai:DiVA.org:su-88598DiVA: diva2:612384