Spiked potentials and quantum toboggans

Details Spiked potentials and quantum toboggans Spiked potentials and quantum toboggans

2006-06-20

arxiv.org/abs/quant-ph/0606166v2

J. Phys. A: Math. Gen. 39 (2006) 13325-13336

Physics

Quantum Physics

revision: 22 pp, 1 fig

Scientific paper

10.1088/0305-4470/39/42/008

Even if the motion of a quantum (quasi-)particle proceeds along a left-right-symmetric (PT-symmetric) curved path in complex plane, the spectrum of bound states may remain physical, i.e., real and bounded below). We propose a generalization. Firstly, we show how the topologically less trivial (tobogganic) contours may be allowed to live on several sheets of a Riemann surface. Secondly, the specification of a scattering regime is formulated for such a class of models.

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