# Barrier penetration in a discrete basis formalism

Source: [Barrier penetration in a discrete basis formalism](<https://www.sota2.com/research/paper/68fa46311e209131ce91e6d6>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T05:40:53.617Z

Authors: K. Hagino

Published: 2023-11-02T01:42:46.000Z

## Abstract

A standard way to solve a Schr\\"odinger equation is to discreteize the radial coordinates and apply a numerical method for a differential equation, such as the Runge-Kutta method or the Numerov method. Here I employ a discrete basis formalism based on a finite mesh method as a simpler alternative, with which the numerical computation can be easily implemented by ordinary linear algebra operations. I compare the numerical convergence of the Numerov integration method to the finite mesh method for calculating penetrabilities of a one-dimensional potential barrier, and show that the latter approach has better convergence properties.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2311.00925>)

[PDF](<https://arxiv.org/pdf/2311.00925.pdf>)