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

Miloslav Znojil
2000 Journal of Physics A: Mathematical and General  
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.
doi:10.1088/0305-4470/33/38/313 fatcat:bhiktqame5bfhimdcfp3krl3fe