# Swanson Hamiltonian: non-PT-symmetry phase

@article{Fernndez2021SwansonHN,
title={Swanson Hamiltonian: non-PT-symmetry phase},
author={Viviano Fern{\'a}ndez and Romina Ram{\'i}rez and Marta Reboiro},
journal={Journal of Physics A: Mathematical and Theoretical},
year={2021},
volume={55}
}
• Published 2 August 2021
• Physics
• Journal of Physics A: Mathematical and Theoretical
In this work, we study the non-Hermitian Swanson Hamiltonian, particularly the non-parity-time symmetry phase. We use the formalism of Gel’fand triplet to construct the generalized eigenfunctions and the corresponding spectrum. Depending on the region of the parameter model space, we show that the Swanson Hamiltonian represents different physical systems, i.e. parabolic barrier, negative mass oscillators. We also discussed the presence of Exceptional Points of infinite order.
4 Citations

### Integral Transforms and $\mathcal{PT}$-symmetric Hamiltonians

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• 2022
The exponential Fourier transform of a given non-Hermitian PT -symmetric potential in the position space is Hermitian . We prove this proposition for any PT -symmetric non-Hermitian Hamiltonians. The

### A Swanson-like Hamiltonian and the inverted harmonic oscillator

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Journal of Physics A: Mathematical and Theoretical
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We deduce the eigenvalues and the eigenvectors of a parameter-dependent Hamiltonian H θ which is closely related to the Swanson Hamiltonian, and we construct bi-coherent states for it. After that, we

### Acta Polytechnica

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In this work, we study the non-hermitian PT-symmetry Swanson Hamiltonian in the framework of the Complex Scaling Method. We show that by applying this method we can work with eigenfunctions that are

• 2022

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