Parametric evolution, addition of boundstates and generalised Lax hierarchies

TL;DR

This paper explores the evolution of eigenstates in reflectionless and more general Schrödinger potentials, establishing a new hierarchy of functions satisfying time-dependent equations to extend the Lax hierarchy framework.

Contribution

It introduces a new hierarchy of functions for time evolution in Schrödinger potentials with non-zero reflection coefficients, extending the Lax hierarchy concept.

Findings

Established a connection between eigenstate evolution in reflectionless and general potentials.

Developed a new hierarchy of functions satisfying time-dependent equations.

Extended the Lax hierarchy to more general potential cases.

Abstract

The connection of the 'time' evolution of the eigenstates of the reflectionless potentials of the Lax hierarchy to the more general case of the 'time' evolution of the eigenstates of the Schroedinger equation for potentials with non-vanishing reflection coefficients is explored. A new hierarchy of functions satisfying 'time' dependent equations is established.