Anti- \(\mathcal{PT}\)-symmetric harmonic oscillator and its relation to the inverted harmonic oscillator
From MaRDI portal
Publication:2106361
DOI10.1016/S0034-4877(22)00083-0MaRDI QIDQ2106361
Rahma Zerimeche, Nadjat Amaouche, Ishak Bouguerche, Mustapha Maamache
Publication date: 14 December 2022
Published in: Reports on Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2204.10780
Cites Work
- Phase transitions in Wick-rotated~ \(\mathcal{PT}\)-symmetric optics
- Operator methods of the parabolic potential barrier
- Quasi-Hermitian operators in quantum mechanics and the variational principle
- The Riemann zeta function and the inverted harmonic oscillator
- Rigged Hilbert spaces and time asymmetry: The case of the upside-down simple harmonic oscillator
- Inverting a normal harmonic oscillator: physical interpretation and applications
- Physics of the inverted harmonic oscillator: From the lowest Landau level to event horizons
- Quantum damped oscillator. II: Bateman's Hamiltonian vs. 2D parabolic potential barrier
- Factorization method and new potentials from the inverted oscillator
- Complex Extension of Quantum Mechanics
- Discrete repulsive oscillator wavefunctions
- Tunnelling process for non-Hermitian systems: the complex-frequency inverted oscillator
- Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
- Non-Hermitian inverted harmonic oscillator-type Hamiltonians generated from supersymmetry with reflections
- Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- Quantum mechanics of damped systems. II. Damping and parabolic potential barrier
- $\mathcal{PT}$-symmetric electronics
- Anti-$\mathcal{PT}$ symmetry for a non-Hermitian Hamiltonian
- QUANTUM STATES OF A GENERALIZED TIME-DEPENDENT INVERTED HARMONIC OSCILLATOR
- Continuous-Representation Theory. I. Postulates of Continuous-Representation Theory
- Time behavior of a Gaussian wave packet accompanying the generalized coherent state for the inverted oscillator
- Coherent and Incoherent States of the Radiation Field
- Equivalence of Semiclassical and Quantum Mechanical Descriptions of Statistical Light Beams