sl(2, ) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues

2000/08/10 by Bijan Bagchi, B. Bagchi, C. Quesne · 10 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebra over a field #Eigenvalues and eigenvectors #Formalism (music) #Hermitian matrix #Lie algebra #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Synthesis and Properties of Aromatic Compounds #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1016/s0375-9601(00)00512-0

published as Phys.Lett. A273 (2000) 285-292 · LaTeX, amssym,14 pages, no figures, to be published in Phys. Lett. A

arxiv created 2000/08/10 · openalex publication_date 2000/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The powerful group theoretical formalism of potential algebras is extended to non-Hermitian Hamiltonians with real eigenvalues by complexifying so(2,1), thereby getting the complex algebra sl(2,\C) or A₁. This leads to new types of both PT-symmetric and non-PT-symmetric Hamiltonians.

Citations

• New set of exactly solvable complex potentials giving the real energies
• Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry
• Supersymmetry and Quantum Mechanics

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• Effective-mass Klein–Gordon equation for non-PT/non-Hermitian generalized Morse potential