# 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} }

## 103 Citations

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

- Mathematics
- 2002

### 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…

### 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…

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

- Physics
- 2009

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

- Physics, Mathematics
- 2010

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

- Physics
- 2009

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

- 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

- MathematicsProceedings 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

- Mathematics
- 1994

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…

### Group theory approach to scattering. IV: Solvable potentials associated with SO(2, 2)

- Mathematics
- 1989

### 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…