Spiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states
Quantum Physics
2009-11-06 v2
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.
Keywords
Cite
@article{arxiv.quant-ph/0002083,
title = {Spiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states},
author = {Miloslav Znojil},
journal= {arXiv preprint arXiv:quant-ph/0002083},
year = {2009}
}
Comments
15 pages and two figures