Abstract
A non-standard generalization of the Bender potentials x 2(ix ɛ) is suggested. The spectra are obtained numerically and some of their particular properties are discussed.
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In fact one can even release the asymptotic straightness condition provided that the contour does not oscillate too rapidly in the asymptotic region. The technical details of equivalence between contour integrability and boundary conditions in infinity are beyond the scope of this article
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Suggested imagination is, of course, consistent only when infinite number of sheets are present
This choice puts a limit on the applicability of the method to ɛ < 2
The energy dependence of the solution is made explicit in the following
M Znojil, Phys. Lett. A342, 36 (2005)
F(x) = (logΓ(x))′ where Γ is the standard Euler gamma function
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Bíla, H. Spectra of \( \mathcal{P}\mathcal{T} \)-symmetric Hamiltonians on tobogganic contours. Pramana - J Phys 73, 307–314 (2009). https://doi.org/10.1007/s12043-009-0122-8
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DOI: https://doi.org/10.1007/s12043-009-0122-8