Observables of Complex PT-Symmetric “Shifted” Potentials

We study complex PT-symmetric potentials, with real eigenvalues, corresponding to a complex coordinate shift (x+ic2) of a real even potential. In this case,the rules to achieve a coherent quantum mechanics are known. They allow the calculation of observables, which are found to be independent on c....

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Bibliographic Details
Published in:Romanian journal of physics 2020, Vol.65
Main Authors: Lombard, Roland J., Mezhoud, R., Yekken, R.
Format: Article
Language:English
Subjects:
Nuclear Theory
Physics
Online Access:Get full text
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Summary:We study complex PT-symmetric potentials, with real eigenvalues, corresponding to a complex coordinate shift (x+ic2) of a real even potential. In this case,the rules to achieve a coherent quantum mechanics are known. They allow the calculation of observables, which are found to be independent on c. This result is illustratedby few analytical or semi analytical examples. On the other hand, trying to test thisproperty numerically faces problems linked to the difficulty of finding the proper solutions of the Schrodinger equation. In particular, the large distance behaviour of the ¨wave functions generates instabilities. As an example, we have studied the (x +ic2)4potential.
ISSN:1221-146X