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}
}

Exponential type complex and non-Hermitian potentials within quantum Hamilton–Jacobi formalism

PT-/non-PT-symmetric and non-Hermitian deformed Morse and Pöschl-Teller potentials are studied first time by quantum Hamilton–Jacobi approach. Energy eigenvalues and eigenfunctions are obtained by

Supersymmetric Solutions of PT-/non-PT-symmetric and Non-Hermitian Central Potentials via Hamiltonian Hierarchy Method

The supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian deformed Morse and Pöschl-Teller potentials are obtained by solving the Schrödinger equation. The Hamiltonian hierarchy method

Generating complex potentials with real eigenvalues in supersymmetric quantum mechanics

In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based

Coherent states for PT-/non-PT-symmetric and non-Hermitian Morse potentials via the path integral method

We discuss the coherent states for PT-/non-PT-symmetric and non-Hermitian generalized Morse potentials obtained by using path integral formalism over the holomorphic coordinates. We transform the

Non Hermitian Hamiltonian with gauge-like transformation

The non Hermitian Hamiltonian is solved for the two quasi-exactly solvable potential by using gauge-like transformation. Possible generalization of our approach is outlined.
...

References

SHOWING 1-10 OF 44 REFERENCES

Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry

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

  • A. BarutC. Frønsdal
  • 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

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

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

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

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