Abstract
Schrödinger equations for ‘quantum toboggans’ with real energies are given the generalized eigenvalue-problem form Hψ = EWψ, 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.
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