International Journal of Theoretical Physics

, Volume 50, Issue 4, pp 982–990 | Cite as

\(\mathcal{CPT}\)-Symmetric Discrete Square Well

Article

Abstract

In an addendum to the recent systematic Hermitization of certain N by N matrix Hamiltonians H (N)(λ) (Znojil in J. Math. Phys. 50:122105, 2009) we propose an amendment H (N)(λ,λ) of the model. The gain is threefold. Firstly, the updated model acquires a natural mathematical meaning of Runge-Kutta approximant to a differential \(\mathcal{PT}\)-symmetric square well in which \(\mathcal{P}\) is parity. Secondly, the appeal of the model in physics is enhanced since the related operator \(\mathcal{C}\) of the so called “charge” (the requirement of observability of which defines the most popular Bender’s metric \(\Theta=\mathcal{PC}\)) becomes also obtainable (and is constructed here) in an elementary antidiagonal matrix form at all N. Last but not least, the original phenomenological energy spectrum is not changed so that the domain of its reality (i.e., the interval of admissible couplings λ∈(−1,1)) remains the same.

Keywords

PT symmetry CPT symmetry Solvable example Discrete model Hidden Hermiticity Generalised parities Charge 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Nuclear Physics Institute ASCRŘežCzech Republic

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