Schroedinger operators with n positive eigenvalues: an explicit construction involving complex valued potentials

TL;DR

This paper presents an explicit method to construct potentials for Schroedinger operators that embed n positive eigenvalues, including real and complex potentials, expanding understanding of spectral properties.

Contribution

It introduces a novel explicit construction for Schroedinger operators with specified positive eigenvalues, including complex potentials, which was not previously available.

Findings

Constructed potentials embed n positive eigenvalues

Potential can be real or complex valued

Method applies to Schroedinger operators on the half-line

Abstract

An explicit construction is provided for embedding n positive eigenvalues in the spectrum of a Schroedinger operator on the half-line with a Dirichlet boundary condition at the origin. The resulting potential is of von Neumann-Wigner type, but can be real valued as well as complex valued.