On eigenfunctions of one-dimensional Schrodinger operator with polynomial potentials

TL;DR

This paper explores the relationship between eigenfunctions of one-dimensional Schrödinger operators with polynomial potentials and eigenfunctions of rank two commuting differential operators, revealing new connections in mathematical physics.

Contribution

It establishes a novel link between eigenfunctions of polynomial potential Schrödinger operators and rank two commuting differential operators.

Findings

Identifies a connection between eigenfunctions of specific Schrödinger operators and commuting differential operators.

Provides insights into the structure of eigenfunctions for polynomial potentials of degree 3 and 4.

Enhances understanding of integrable systems in mathematical physics.

Abstract

In this paper we point out an connection between eigenfunctions of one-dimensional Schrodinger operator with polynomial potentials of degree 3, 4 and eigenfunctions of rank two commuting ordinary differential operators.