Eigenstates of the Vorticity Operator: The Creation and Annihilation of Vortex States in Two Dimensions

TL;DR

This paper develops a quantum mechanical framework for vortices in two-dimensional superfluid helium-4, defining creation and annihilation operators, constructing wavefunctions, and proposing a Hamiltonian for vortex states.

Contribution

It introduces a novel quantum description of vortex states, including explicit operators, wavefunctions, and a Hamiltonian, advancing understanding of vortex dynamics in superfluids.

Findings

Defined vortex creation and annihilation operators

Constructed explicit vortex wavefunctions

Proposed a Hamiltonian for vortex states

Abstract

A quantum mechanical description of vortices in two dimensional superfluid $^4$He flims is presented. Single vortex creation and annihilation operators are defined and wavefunctions for these states are explicitly constructed. A hamitonian for these states is then proposed.