Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework

@article{Bagchi2002NonHermitianHW,
  title={Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework},
  author={Bijan Bagchi and C Quesne},
  journal={Physics Letters A},
  year={2002},
  volume={300},
  pages={18-26}
}

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References

SHOWING 1-10 OF 39 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

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

Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum

We give a necessary and sufficient condition for the reality of the spectrum of a non-Hermitian Hamiltonian admitting a complete set of biorthonormal eigenvectors.

Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian

We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in

PT symmetric nonpolynomial oscillators and hyperbolic potential with two known real eigenvalues in a SUSY framework

Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasi-exactly solvable PT-symmetric potentials