# Garrett approximation revisited

## TL;DR

This paper revisits three variants of the Garrett approximation for quantum wells, analyzing their accuracy for symmetric and asymmetric cases, and finds that simpler variants are surprisingly more precise, with applications discussed.

## Contribution

The study provides a comparative analysis of Garrett approximation variants, highlighting the accuracy of simpler forms for quantum well problems.

## Key findings

- Simplest variants of Garrett approximation are most accurate.
- Accuracy varies between symmetric and asymmetric wells.
- Applications to quantum dots and neutron guides are discussed.

## Abstract

Three variants of the Garrett approximation are studied and their accuracy is analyzed, for symmetric and asymmetric square wells. Quite surprisingly, the simplest variants are also the most accurate. The applications to quantum wells, quantum dots and capillary neutron guides are briefly discussed.