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

Miloslav Znojil
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Abstract

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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Miloslav Znojil. 2000-08-24. Spiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states. https://doi.org/10.1088/0305-4470%2F33%2F38%2F313

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