Hierarchical Wave Functions Revisited

TL;DR

This paper revisits hierarchical wave functions on spherical and toroidal geometries, simplifying their forms and solving the open problem of constructing quasielectron wave functions on a torus.

Contribution

It introduces simplified forms of hierarchical wave functions and provides a solution for constructing quasielectron excitations on a torus.

Findings

Simplified wave functions on sphere and torus

Constructed quasielectron wave functions on a torus

Enhanced understanding of hierarchical wave functions

Abstract

We study the hierarchical wave functions on a sphere and on a torus. We simplify some wave functions on a sphere or a torus using the analytic properties of wave functions. The open question, the construction of the wave function for quasielectron excitations on a torus, is also solved in this paper.