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\(\mathcal{PT}\)-symmetric quantum toboggans. (English) Zbl 1222.81170

Summary: We note that within \(\mathcal{PT}\)-symmetric quantum mechanics which admits complex coordinates, the classical toboggans with descending spiral trajectories \(C(s)\) possess quantum analogues whose spirals \(C(s)\) are wound round the branch-points. We show that and how the simplest tobogganic bound states may be constructed in closed form.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81U15 Exactly and quasi-solvable systems arising in quantum theory
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