A short note on the presence of spurious states in finite basis approximations

TL;DR

This paper discusses the origin of spurious solutions in finite basis approximations of operators with continuum and point spectra, and proposes a simple method to identify these false solutions.

Contribution

It introduces a straightforward technique to distinguish genuine solutions from spurious ones in finite basis approximations.

Findings

Identifies conditions leading to spurious solutions.

Proposes a simple identification method.

Enhances reliability of finite basis approximations.

Abstract

The genesis of spurious solutions in finite basis approximations to operators which possess a continuum and a point spectrum is discussed and a simple solution for identifying these solutions is suggested.