Schroedinger equations with indefinite effective mass

TL;DR

This paper investigates the stability of quantum systems with position- and energy-dependent effective mass, demonstrating that such systems can remain stable even when the effective mass becomes negative in certain regions.

Contribution

It introduces simplified models to analyze the stability of quantum particles with indefinite effective mass, showing stability despite negative mass values.

Findings

Systems can be stable with negative effective mass regions.

Effective mass can depend on position and energy without causing instability.

Simplified models effectively analyze the concept of indefinite effective mass.

Abstract

The consistency of the concept of quantum (quasi)particles possessing effective mass which is both position- and excitation-dependent is analyzed via simplified models. It is shown that the system may be stable even when the effective mass m=m(x,E) itself acquires negative values in a limited range of coordinates x and energies E.