Further analysis of the connected moments expansion

TL;DR

This paper investigates the limitations of the connected moments expansion in quantum mechanics by analyzing simple systems like two-level systems and oscillators, revealing conditions where the main equations break down.

Contribution

It provides a critical assessment of the connected moments expansion's validity across different quantum systems, highlighting its limitations.

Findings

Main equations of the expansion are invalid under certain conditions.

Breakdown occurs in two-level systems and harmonic oscillator models.

Highlights the need for caution when applying the expansion to complex systems.

Abstract

We apply the connected moments expansion to simple quantum--mechanical examples and show that under some conditions the main equations of the approach are no longer valid. In particular we consider two--level systems, the harmonic oscillator and the pure quartic oscillator.