Abstract
A generalization of the concept of PT—symmetric Hamiltonians H = p2 + V (x) is presented. For the usual analytic potentials V (x) (with singularities) and for the recently widely accepted ‘PT—symmetric’ asymptotic boundary conditions for wave functions ψ(x) (selected inside a pair of complex wedges generalizing the usual x → ±∞ asymptotics), non-equivalent quantum toboggans are defined as integrated along topologically different paths C of coordinates x ε Cl.
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