# 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} }

## 59 Citations

### Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials

- Physics, Mathematics
- 2012

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

- Physics
- 2007

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…

### Real spectra for the non-Hermitian Dirac equation in 1+1 dimensions with the most general coupling

- Physics
- 2009

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

- Physics
- 2004

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…

### Supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian screened Coulomb potential via Hamiltonian hierarchy inspired variational method

- Physics
- 2007

The supersymmetric solutions of PT -symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schrödinger equation for the Exponential-Cosine Screened Coulomb…

### Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians

- Mathematics
- 2002

We give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonalization with finite-dimensional diagonal…

### Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States ?

- Physics
- 2010

A new class of non-Hermitian Hamiltonians with real spectrum, which are writ- ten as a real linear combination of su(2) generators in the form H = !J3 + �J + �J+, � 6 �, is analyzed. The metrics…

### DARBOUX TRANSFORMATION FOR THE ONE-DIMENSIONAL STATIONARY DIRAC EQUATION WITH NON-HERMITIAN INTERACTION

- Physics, Mathematics
- 2006

The Darboux algorithm is applied to an exactly solvable one-dimensional stationary Dirac equation, with non-Hermitian, pseudoscalar interaction V0(x). This generates a hierarchy of exactly solvable…

## References

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- Mathematics
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### 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…

### Generating complex potentials with real eigenvalues in supersymmetric quantum mechanics

- Mathematics
- 2001

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…

### Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex -invariant potential

- Mathematics, Physics
- 2001

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

- Mathematics
- 2001

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

- Physics
- 2001

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

- Mathematics
- 2002

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…