Identification of observables in quantum toboggans

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.

25 pp

References in corpus (25)

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Cited by in corpus (7)

• Three-Hilbert-Space Formulation of Quantum Mechanics
• Topology-controlled spectra of imaginary cubic oscillators in the large-L approach
• Sturm-Schroedinger equations: formula for metric
• Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces
• Ad hoc physical Hilbert spaces in Quantum Mechanics
• Planarizable Supersymmetric Quantum Toboggans
• PT-symmetric Sturmians