Anomalous doublets of states in a PT symmetric quantum model

Abstract

We complexify one of the Natanzon's exactly solvable potentials in PT symmetric manner and discover that it supports the pairs of bound states with the same number of nodal zeros. This could indicate that the Sturm Liouville oscillation theorem does not admit an immediate generalization.

13 pages, re-submitted to Phys. Lett. A, thoroughly revised

References in corpus (2)

• Comprehensive analysis of conditionally exactly solvable models
• Exactly solvable three-body Calogero-type model with translucent two-body barriers

Cited by in corpus (5)

• PT symmetry of a conditionally exactly solvable potential
• An exactly solvable PT symmetric potential from the Natanzon class
• Lower bound of minimal time evolution in quantum mechanics
• Quantum Dynamical Algebra SU(1,1) in One-Dimensional Exactly Solvable Potentials
• "Striped" Rectangular Rigid Box with Hermitian and non-Hermitian $\mathcal{P}\mathcal{T}$ Symmetric Potentials