Non-hermitian Hamiltonians and Painlev\'e IV equation with real parameters

TL;DR

This paper explores complex solutions to the Painleve IV equation with real parameters using higher-order supersymmetric quantum mechanics, analyzing the algebraic structure, eigenfunctions, and spectra of associated non-hermitian Hamiltonians.

Contribution

It introduces a method to generate complex solutions to Painleve IV with real parameters via higher-order supersymmetric quantum mechanics, and studies the properties of related non-hermitian Hamiltonians.

Findings

Derived new families of complex solutions to Painleve IV.

Analyzed the algebraic structure of non-hermitian Hamiltonians.

Examined eigenfunctions and energy spectra of the Hamiltonians.

Abstract

In this letter we will use higher-order supersymmetric quantum mechanics to obtain several families of complex solutions of the Painleve IV equation with real parameters. We shall also study the algebraic structure, the eigenfunctions and the energy spectra of the corresponding non-hermitian Hamiltonians.