# PT-symmetric operators and metastable states of the 1D relativistic oscillators

@article{Giachetti2010PTsymmetricOA, title={PT-symmetric operators and metastable states of the 1D relativistic oscillators}, author={Riccardo Giachetti and Vincenzo Grecchi}, journal={arXiv: Mathematical Physics}, year={2010} }

We consider the one-dimensional Dirac equation for the harmonic oscillator and the associated second order separated operators giving the resonances of the problem by complex dilation. The same operators have unique extensions as closed PT-symmetric operators defining infinite positive energy levels converging to the Schroedinger ones as c tends to infinity. Such energy levels and their eigenfunctions give directly a definite choice of metastable states of the problem. Precise numerical…

## 11 Citations

Level crossings in a PT-symmetric double well

- Mathematics
- 2015

We consider the eigenvalues (levels) and the eigenfunctions (states) of a one-parameter family of Hamiltonians with a PT-symmetric double well. We call nodes the zeros of the states that are stable…

Bender-Wu singularities

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- 2016

We consider the properties of the family of double well quantum Hamiltonians Hħ = − ħ2 (d2/dx2) + i(x3 − x), x ∈ ℝ, ħ > 0, starting from the resonances of the cubic oscillator Hϵ = − (d2/dx2) + x2 +…

Dynamical system of relativistic particle under one dimensional harmonic oscillator potential

- Physics
- 2021

Dynamical system of a relativistic particle under harmonic oscillator potential was considered through its stability. We first construct the Hamiltonian of the system, which represents the dynamic…

The eigenvalue problem of one-dimensional Dirac operator

- PhysicsTheoretical Chemistry Accounts
- 2020

The properties of the eigenvalue problem of the one-dimensional Dirac operator are discussed in terms of the mutual relations between vector, scalar and pseudo-scalar contributions to the potential.…

$\mathcal{PT}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions

- Physics, Mathematics
- 2013

In this article, we have introduced a $\mathcal{PT}$ symmetric non-Hermitian Hamiltonian model which is given as $\hat{\mathcal{H}}=\omega (\hat{b}^{\dag}\hat{b}+1/2)+ \alpha…

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