2008/03/31 by Miloslav Znojil
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/21/215304
published as J. Phys. A: Math. Theor. 41 (2008) 215304 · 25 pp
arxiv created 2008/04/21 · openalex publication_date 2008/05/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Schrödinger equations for ‘quantum toboggans’ with real energies are given the generalized eigenvalue-problem form H ψ = EW ψ, where H ≠ H † and W ≠ W † ≠ I . The consistent probabilistic interpretation of these models is provided. The new double-series formula for the necessary ad hoc metric Θ = Θ( H , W ) is derived which defines the acceptable inner products in the physical Hilbert space of states. The formula degenerates to the usual single series in the non-tobogganic trivial-weight limit W → I .