Supersymmetry with self-consistent Schrödinger–Poisson equations: finding partner potentials and breaking symmetry

Abstract

It is shown that isospectral Hamiltonians and partner potentials can be found for self-consistent solutions of the Schrödinger and Poisson equations in the presence of identical non-interacting electrons. Perturbation of these systems by an external electric field can be used to break symmetry and spectrally distinguish between states. For a given pair of partner potentials, symmetry may also be broken by a change of electron density or temperature.

Keywords

• supersymmetric quantum mechanics
• supersymmetry
• self-consistent Schrödinger equation
• Schrödinger–Poisson equation