AUTHOR(S):

Suha Tuna, Metin Demiralp

TITLE

Validity and Failure of the Autonomy Imposition on the Eigenfunctions in Zero Interval Limit Perturbation Expansion for Hilbert-Schmidt Integral Operators

KEYWORDS

Integral operators, eigenfunctions, perturbation expansion, autonomy

ABSTRACT

In this paper, we focus on the autonomy issue in the perturbation expansions of eigenfunctions. We consider the zero interval limit perturbation expansion of a Hilbert-Schmidt Integral Operator here and the autonomy means that the eigenfunction depends on the perturbation parameter not only through the independent variable argument but via an additional argument which just the perturbation parameter. Our purpose is to show that the autonomy puts an important restriction on the kernel of the operator and the resulting perturbation series fails to exist unless a specific and appropriate kernel is used. The proof is also supported by the given illustrative implementations.

Cite this paper

Suha Tuna, Metin Demiralp. (2016) Validity and Failure of the Autonomy Imposition on the Eigenfunctions in Zero Interval Limit Perturbation Expansion for Hilbert-Schmidt Integral Operators. International Journal of Applied Physics, 1, 42-48