Non-Hermitian Oscillator and R-deformed Heisenberg Algebra
arXiv:1301.0716 · doi:10.1063/1.4773097
Abstract
A non-Hermitian generalized oscillator model, generally known as the Swanson model, has been studied in the framework of R-deformed Heisenberg algebra. The non-Hermitian Hamiltonian is diagonalized by generalized Bogoliubov transformation. A set of deformed creation annihilation operators is introduced whose algebra shows that the transformed Hamiltonian has conformal symmetry. The spectrum is obtained using algebraic technique. The superconformal structure of the system is also worked out in detail. An anomaly related to the spectrum of the Hermitian counterpart of the non-Hermitian Hamiltonian with generalized ladder operators is shown to occur and is discussed in position dependent mass scenario.
References in corpus (9)
- Making Sense of Non-Hermitian Hamiltonians
- Hidden supersymmetry in quantum bosonic systems
- Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
- Supersymmetric Quantum Mechanics with Reflections
- Generalized Swanson models and their solutions
- A generalized non-Hermitian oscillator Hamiltonian, N-fold supersymmetry and position-dependent mass models
- Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
- Position-dependent mass models and their nonlinear characterization
- Deformed su(1,1) Algebra as a Model for Quantum Oscillators