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Pramana

, 73:307 | Cite as

Spectra of \( \mathcal{P}\mathcal{T} \)-symmetric Hamiltonians on tobogganic contours

  • Hynek Bíla
Article

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.

Keywords

Quantum toboggans \(\mathcal{P}\mathcal{T}\) symmetry complex integration contours 

PACS Nos

02.60.Lj 03.65.Ge 

References

  1. [1]
    C M Bender, S Boettcher and P N Meisinger, J. Math. Phys. 40, 2201 (1999)zbMATHCrossRefMathSciNetADSGoogle Scholar
  2. [1a]
    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 articleGoogle Scholar
  3. [2]
    F J Dyson, Phys. Rev. 85, 631 (1952)zbMATHCrossRefMathSciNetADSGoogle Scholar
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    C M Bender, D C Brody and H F Jones, Am. J. Phys. 71, 1095 (2003)CrossRefMathSciNetADSGoogle Scholar
  5. [3a]
    Suggested imagination is, of course, consistent only when infinite number of sheets are presentGoogle Scholar
  6. [3b]
    This choice puts a limit on the applicability of the method to ɛ < 2Google Scholar
  7. [3c]
    The energy dependence of the solution is made explicit in the followingGoogle Scholar
  8. [4]
    M Znojil, Phys. Lett. A342, 36 (2005)MathSciNetADSGoogle Scholar
  9. [4a]
    F(x) = (logΓ(x))′ where Γ is the standard Euler gamma functionGoogle Scholar

Copyright information

© Indian Academy of Sciences 2009

Authors and Affiliations

  1. 1.Ústav jaderné fyziky AV ČRŘež, PragueCzech Republic

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