Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
arXiv:0705.2868 · doi:10.1088/1751-8113/40/30/F07
Abstract
The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian -symmetric part, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it opens the way towards the construction of generalized non-Hermitian (not necessarily -symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.
arXiv comment11 pages, no figure; changes in title and in paragraphs 3 and 5; final published version
References in corpus (18)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Complex Extension of Quantum Mechanics
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
- Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
- Physical Aspects of Pseudo-Hermitian and -Symmetric Quantum Mechanics
- Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
- On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts
- Quasi-Hermiticity in infinite-dimensional Hilbert spaces
- Pseudo-Hermiticity and some consequences of a generalized quantum condition
- Operator equations and Moyal products -- metrics in quasi-hermitian quantum mechanics
- Moyal products -- a new perspective on quasi-hermitian quantum mechanics
- The Hilbert-Space Structure of Non-Hermitian Theories with Real Spectra
- Quantization and Conformal Properties of a Generalized Calogero Model
- Trigonometric identities, angular Schrödinger equations and a new family of solvable models
- Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?
- Universal properties of conformal quantum many-body systems
- sl(2,R) symmetry and solvable multiboson systems
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- Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
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