Spiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states

Details Spiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states Spiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states

2000-02-26

arxiv.org/abs/quant-ph/0002083v2

J. Phys. A: Math. Gen. 33 (2000) 6825 - 6833

Physics

Quantum Physics

15 pages and two figures

Scientific paper

10.1088/0305-4470/33/38/313

We show that the potential wells with a central spike V(x) = x^{10} + a x^8 + b x^6+ c x^4 + d x^2 + f/x^2 possess arbitrary finite multiplets of elementary exact bound states. The strong asymptotic growth of V(x) implies an ambiguity in the PT-symmetric quantization via complex boundary conditions but the three eligible recipes coincide at our exceptional solutions.

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