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Pramana

, 73:329 | Cite as

Spontaneous breakdown of \( \mathcal{P}\mathcal{T} \) symmetry in the complex Coulomb potential

  • G. Lévai
Article

Abstract

The \( \mathcal{P}\mathcal{T} \) symmetry of the Coulomb potential and its solutions are studied along trajectories satisfying the \( \mathcal{P}\mathcal{T} \) symmetry requirement. It is shown that with appropriate normalization constant the general solutions can be chosen \( \mathcal{P}\mathcal{T} \) -symmetric if the L parameter that corresponds to angular momentum in the Hermitian case is real. \( \mathcal{P}\mathcal{T} \) symmetry is spontaneously broken, however, for complex L values of the form L = −1/2 + iλ. In this case the potential remains \( \mathcal{P}\mathcal{T} \) -symmetric, while the two independent solutions are transformed to each other by the \( \mathcal{P}\mathcal{T} \) operation and at the same time, the two series of discrete energy eigenvalues turn into each other’s complex conjugate.

Keywords

Spontaneous breakdown of \(\mathcal{P}\mathcal{T}\) symmetry Coulomb potential complex energy eigenvalues 

PACS Nos

03.65.Ge 03.65.Nk 11.30.Er 

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Copyright information

© Indian Academy of Sciences 2009

Authors and Affiliations

  1. 1.Institute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI)DebrecenHungary

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