Identification of observables in quantum toboggans

TL;DR

This paper extends the framework for defining observables in non-Hermitian quantum systems to quantum toboggans, providing a method to identify metrics and observables ensuring consistent probabilistic interpretation.

Contribution

It introduces a systematic approach to determine observables in quantum toboggans by rectifying integration paths and deriving metric operators.

Findings

Derived the generalized eigenvalue problem for quantum toboggans.

Developed a double-series representation for metric operators.

Extended the observable identification framework to non-Hermitian tobogganic systems.

Abstract

Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of states. The recipe is extended here to quantum toboggans. In the first step the tobogganic integration path is rectified and the Schroedinger equation is given the generalized eigenvalue-problem form. In the second step the general double-series representation of the eligible metric operators is derived.