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

@article{Bagchi2000sl2CA,
title={sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues},
author={Bijan Bagchi and C Quesne},
journal={Physics Letters A},
year={2000},
volume={273},
pages={285-292}
}
• Published 10 August 2000
• Mathematics
• Physics Letters A
103 Citations

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References

SHOWING 1-10 OF 44 REFERENCES

Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry

• Mathematics
• 1998
The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new

On non-compact groups. II. Representations of the 2+1 Lorentz group

• Mathematics
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
• 1965
A simple algebraic method based on multispinors with a complex number of indices is used to obtain the linear (and unitary) representations of non-com pact groups. The method is illustrated in the

LETTER TO THE EDITOR: A new PT-symmetric complex Hamiltonian with a real spectrum

• Mathematics, Physics
• 2000
We construct an isospectrum system in terms of a real and a complex potential to show that the underlying PT -symmetric complex Hamiltonian possesses a real spectrum which is shared by its real

Solvable potentials associated with su(1,1) algebras: a systematic study

We consider a specific differential realization of the su(1,1) algebra and use it to explore such algebraic structures associated with shape-invariant potentials. Our approach combines elements of

SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra

• Physics
• 1999
We extend the standard intertwining relations used in supersymmetrical (SUSY) quantum mechanics which involve real superpotentials to complex superpotentials. This allows us to deal with a large

Dynamical Groups and Spectrum Generating Algebras

• Physics
• 1971
This book contains an up-to-date review on dynamical groups, spectrum generating algebras and spectrum supersymmetries, and their application in atomic and molecular physics, nuclear physics,

The potential group approach and hypergeometric differential equations

• Mathematics
• 1990
This paper proposes a generalized realization of the potential groups SO(2,1) and SO(2,2) to describe the confluent hypergeometric and the hypergeometric equations, respectively. It implies that the