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Related Experiment Video

Updated: May 18, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Lagrange-mesh calculations in momentum space.

Gwendolyn Lacroix¹, Claude Semay, Fabien Buisseret

¹Service de Physique Nucléaire et Subnucléaire, Université de Mons, Académie universitaire Wallonie-Bruxelles, Mons, Belgium. gwendolyn.lacroix@umons.ac.be

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

The Lagrange-mesh method efficiently solves quantum eigenequations in both configuration and momentum spaces. This accurate technique simplifies calculations, particularly for the kinetic operator, and computes observables effectively.

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Area of Science:

Computational Physics
Quantum Mechanics
Numerical Methods

Background:

The Lagrange-mesh method offers a robust approach for solving eigenequations in configuration space.
Existing methods often face challenges in computational efficiency and implementation complexity.

Purpose of the Study:

To adapt the Lagrange-mesh method for solving eigenequations in momentum space.
To maintain the accuracy and ease of implementation of the original configuration-space method.
To demonstrate the efficient computation of observables and wave functions in both spaces.

Main Methods:

Utilizing a Gauss quadrature rule for potential evaluation at mesh points.
Expanding eigenfunctions using regularized Lagrange functions.
Adapting the method to momentum space, resulting in a diagonal kinetic operator.

Main Results:

The adapted Lagrange-mesh method successfully solves eigenequations in momentum space with high accuracy.
The kinetic operator becomes a diagonal matrix in momentum space, simplifying calculations.
Observables and wave functions in both configuration and momentum spaces are computed efficiently.

Conclusions:

The Lagrange-mesh method is a versatile and accurate tool for quantum mechanical eigenequations in both configuration and momentum spaces.
The adaptation to momentum space retains the method's practical advantages.
The study validates the method's performance with Gaussian and Yukawa potentials.