Compact, orthogonal, and complete basis sets for solving the Schrodinger equation

TL;DR

This paper introduces orthlets, a new local, compact, and orthogonal basis set for solving the Schrödinger equation, capable of efficiently representing systems with singularities.

Contribution

The paper proposes orthlets, a novel adaptable basis set that improves the representation of quantum systems, especially near singularities, by being local, orthogonal, and customizable.

Findings

Orthlets are local and orthogonal basis functions.

Orthlets can adapt to singular behaviors within the system.

The basis set enhances the efficiency of solving the Schrödinger equation.

Abstract

We present a new type of basis set which is local, compact, and orthogonal. The basis functions, called orthlets, are centered at the sites of a lattice and are specifically adapted to represent the system being studied. The adaptability includes the ability to have singular behavior within an orthlet, allowing a single orthlet to represent a function in the vicinity of a singularity.