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