Test of dilute gas approximation in quantum mechanical model

TL;DR

This paper examines the limitations of the dilute gas approximation in a quantum mechanical model using large instantons, revealing discrepancies with other methods and issues with limiting behavior.

Contribution

It demonstrates that the dilute gas approximation fails to accurately describe the system when instantons are large, challenging its validity in certain quantum models.

Findings

Dilute gas approximation does not match linear combination of atomic orbitals results.

The approximation fails to show proper limiting behavior for large instantons.

Results question the general applicability of dilute gas approximation in quantum models.

Abstract

The validity of dilute gas approximation is explored by making use of the large-sized instanton in quantum mechanical model. It is shown that the Euclidean probability amplitude derived through a dilute gas approximation not only cannot explain the result of the linear combination of atomic orbitals approximation, but also does not exhibit a proper limiting case when the size of instanton is very large.