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

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.

15 pages and two figures

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• Quantum toboggans
• Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to $p^2-i{x}^3$
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• Solvable PT symmetric Hamiltonians
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• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• Quasi-exact minus-quartic oscillators in strong-core regime
• Avoided level crossings in quasi-exact approach