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.

PACS numbers: 03.65.−w, 03.65.Ca, 03.65.Db

Print publication: Issue 21 (30 May 2008)
Received 4 March 2008, in final form 15 April 2008
Published 8 May 2008