Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0407132 · Czechoslovak Journal of Physics

The Physical Interpretation of PT-invariant Potentials

Stefan Weigert

Published Oct 1, 2004• 21 citations
arXivHTMLPDF
DOI
10.1023/b:cjop.0000044016.95629.a7

Related papers

A PT-invariant potential with complex QES eigenvalues

Avinash Khare, Bhabani Prasad Mandal

arXiv:quant-ph/0006126•Physics Letters A•Jul 1, 2000•165 citations

Anti-PT Transformations and Complex PT-Symmetric Superpartners

S. Kartal, Taha Koohrokhi, Ali Mohammadi

Abstract A quantum mechanical system with unbroken super-and parity-time (PT)-symmetry is derived and analyzed. Here, we propose a new formalism to construct the complex PT-symmetric superpartners by extending the additive shape invariant potentials to the complex domain. The probabilistic interpretation of a PT-symmetric quantum theory is correlated with the calculation of a new linear operator called the C operator, instead of complex conjugation in conventional quantum mechanics. At the present work, we introduce an anti-PT (A PT) conjugation to redefine a new version of the inner product without any additional considerations. This PT-supersymmetric quantum mechanics, satisfies essential requirements such as completeness, orthonormality as well as probabilistic interpretation.

•Sep 7, 2021•0 citations

A new solvable complex PT-symmetric potential

Zafar Ahmed, D. C. Ghosh, Joseph Amal Nathan

arXiv:1502.04838•Physics Letters A•Apr 25, 2015•12 citations

Algebraic and scattering aspects of a 𝒫𝒯-symmetric solvable potential

GÉZA LÉVAI, F. Cannata, Alberto Ventura

We study a particular solvable potential and analyse the effect of 𝒫𝒯 symmetry on its bound state as well as scattering solutions. We determine the transmission and reflection coefficients for the 𝒫𝒯-symmetric case and also formulate the problem in terms of an SU (1,1) potential group, which allows unified treatment of the discrete and the continuous spectra in a natural way. We find that (bound and scattering) states of the 𝒫𝒯-symmetric problem supply a basis for the unitary irreducible representations of the SU (1,1) potential group, and this gives a straightforward group theoretical interpretation of the fact that the (complex) 𝒫𝒯-invariant potential has a real energy spectrum.

Journal of Physics A Mathematical and General•Jan 18, 2001•82 citations

The Coulomb potential and the paradoxes of PT symmetrization

Miloslav Znojil

arXiv:1204.1257•Journal of Engineering Mathematics•Nov 21, 2012•0 citations

The Linear Complex PT Symmetric Potential

R.J. Lombard, R. Mezhoud

•Jan 1, 2017•2 citations
Abstract A quantum mechanical system with unbroken super-and parity-time (PT)-symmetry is derived and analyzed. Here, we propose a new formalism to construct the complex PT-symmetric superpartners by extending the additive shape invariant potentials to the complex domain. The probabilistic interpretation of a PT-symmetric quantum theory is correlated with the calculation of a new linear operator called the C operator, instead of complex conjugation in conventional quantum mechanics. At the present work, we introduce an anti-PT (A PT) conjugation to redefine a new version of the inner product without any additional considerations. This PT-supersymmetric quantum mechanics, satisfies essential requirements such as completeness, orthonormality as well as probabilistic interpretation.
We study a particular solvable potential and analyse the effect of 𝒫𝒯 symmetry on its bound state as well as scattering solutions. We determine the transmission and reflection coefficients for the 𝒫𝒯-symmetric case and also formulate the problem in terms of an SU (1,1) potential group, which allows unified treatment of the discrete and the continuous spectra in a natural way. We find that (bound and scattering) states of the 𝒫𝒯-symmetric problem supply a basis for the unitary irreducible representations of the SU (1,1) potential group, and this gives a straightforward group theoretical interpretation of the fact that the (complex) 𝒫𝒯-invariant potential has a real energy spectrum.