Spiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states
Miloslav Znojil
Abstract
We show that the potential wells with a central spike V(x) = x10 + a x8 + b x6+ c x4 + d x2 + f/x2 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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