TL;DR
This paper explores PT-symmetric Sturmian bound states in non-Hermitian Sturm-Schroedinger equations, proposing a new metric formula to restore proper probabilistic interpretation, exemplified with a PT-symmetrized Coulomb potential.
Contribution
It introduces a novel approach to define a consistent probabilistic framework for PT-symmetric Sturmian states using a new metric formula.
Findings
Successful formulation of a new metric for PT-symmetric systems
Application to PT-symmetrized Coulomb potential demonstrates effectiveness
Restoration of probabilistic interpretation in non-Hermitian quantum systems
Abstract
Sturmian bound states emerging at a fixed energy and numbered by a complete set of real eigencouplings are considered. For Sturm-Schroedinger equations which are manifestly non-Hermitian we outline the way along which the correct probabilistic interpretation of the system can constructively be re-established via a new formula for the metric. PT-symmetrized Coulomb potential is chosen for illustration purposes.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Quantum chaos and dynamical systems