Rectifiable PT -symmetric Quantum Toboggans with Two 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.

Keywords

• quantum bound-state models
• wave-functions with branch-points
• complex-contour coordinates
• PT-symmetry
• tobogganic Hamiltonians
• winding descriptors
• single-sheet maps
• Sturm-Schrödinger equations