Dimensionless equations in non-relativistic quantum mechanics

TL;DR

Using dimensionless equations in non-relativistic quantum mechanics simplifies models, highlights key parameters, reduces numerical errors, and aids in perturbation theory analysis, enhancing both analytical and computational approaches.

Contribution

This paper emphasizes the advantages of adopting dimensionless equations, illustrating their benefits for simplifying models and improving numerical and analytical methods in quantum mechanics.

Findings

Dimensionless equations are simpler and reveal relevant parameters.

They reduce round-off errors in numerical computations.

They facilitate perturbation theory applications.

Abstract

We discuss the numerous advantages of using dimensionless equations in non-relativistic quantum mechanics. Dimensionless equations are considerably simpler and reveal the number of relevant parameters in the models. They are less prone to round-off errors when applying numerical methods because all the quantities are of the other of unity. A dimensionless equation facilitates the application of perturbation theory and provides a glimpse of the sort of solution we are going to obtain beforehand.