Rectifiable PT-symmetric Quantum Toboggans with Two Branch Points

TL;DR

This paper explores complex-contour quantum toboggans with two branch points, demonstrating that a suitable change of variables simplifies their numerical solution by transforming multi-sheeted domains into single-sheeted ones.

Contribution

It introduces a method to simplify the numerical analysis of complex quantum toboggans with multiple branch points through a strategic change of variables.

Findings

Complex-contour quantum toboggans can be effectively analyzed using variable transformations.

The method reduces multi-sheeted problems to single-sheeted domains, facilitating numerical solutions.

The approach enhances understanding of PT-symmetric quantum systems with multiple branch points.

Abstract

Certain complex-contour (a.k.a. quantum-toboggan) generalizations of Schroedinger's bound-state problem are reviewed and studied in detail. Our key message is that the practical numerical solution of these atypical eigenvalue problems may perceivably be facilitated via an appropriate complex change of variables which maps their multi-sheeted complex domain of definition to a suitable single-sheeted complex plane.