New formulae for the Aharonov-Bohm wave operators

TL;DR

This paper derives explicit formulas for wave operators in Schrödinger equations with Aharonov-Bohm magnetic fields, linking them to dilation generators and the Laplacian, enhancing understanding of quantum scattering in such fields.

Contribution

It introduces new explicit formulae for Aharonov-Bohm wave operators expressed via dilation generators and the Laplacian, providing a clearer analytical framework.

Findings

Wave operators are expressed explicitly in terms of dilation generators and Laplacian.

The results facilitate better analytical understanding of quantum scattering with magnetic flux.

The formulas may simplify calculations in related quantum physics problems.

Abstract

It is proved that the wave operators corresponding to Schroedinger operators with Aharonov-Bohm type magnetic fields can be rewritten in terms of explicit functions of the generator of dilations and of the Laplacian.