Completeness theorem for the system of eigenfunctions of the complex Schr\"odinger operator $\mathscr{L}_c=-d^2/dx^2+cx^\alpha$

Sergey Tumanov

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arXiv · 2101.01680

Completeness theorem for the system of eigenfunctions of the complex Schr\"odinger operator $\mathscr{L}_c=-d^2/dx^2+cx^\alpha$

Sergey Tumanov

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Abstract

The completeness of the system of eigenfunctions of the complex Schr\"odinger operator $\mathscr{L}_c=-d^2/dx^2+cx^\alpha$ on the semi-axis with Dirichlet boundary conditions is proved for $\alpha\in(0,2)$ and $|\arg c|<2\pi\alpha/(\alpha+2)+\Delta t(\alpha)$ with some $\Delta t(\alpha)>0$.

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BibTeX RIS

Sergey Tumanov. 2021-01-05. Completeness theorem for the system of eigenfunctions of the complex Schr\"odinger operator $\mathscr{L}_c=-d^2/dx^2+cx^\alpha$. https://arxiv.org/abs/2101.01680

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