$\mathcal{D}$-deformed harmonic oscillators

Abstract

We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms of $\mathcal{D}$-pseudo bosons. They all give rise to exactly solvable models, described by non self-adjoint hamiltonians whose eigenvalues and eigenvectors can be found adopting the quite general framework of the so-called $\mathcal{D}$-pseudo bosons. In particular, we show that several models previously introduced in the literature perfectly fit into this scheme.

in press in International Journal of Theoretical Physics

References in corpus (15)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• On the metric operator for the imaginary cubic oscillator
• From self-adjoint to non self-adjoint harmonic oscillators: physical consequences and mathematical pitfalls
• Non-self-adjoint hamiltonians defined by Riesz bases
• More mathematics for pseudo-bosons
• $J$-self-adjoint operators with $\mathcal{C}$-symmetries: extension theory approach
• A non self-adjoint model on a two dimensional noncommutative space with unbound metric
• Quadratic PT-symmetric operators with real spectrum and similarity to self-adjoint operators
• Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
• Model pseudofermionic systems: connections with exceptional points
• Non Hermitian Operators with Real Spectrum in Quantum Mechanics
• A possible method for non-Hermitian and non-$PT$-symmetric Hamiltonian systems
• Weak commutation relations of unbounded operators: nonlinear extensions
• Weak commutation relations of unbounded operators and applications

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• New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalization
• Appearances of pseudo-bosons from Black-Scholes equation
• Finite-dimensional pseudo-bosons: a non-Hermitian version of the truncated harmonic oscillator
• Non self-adjoint operators with real spectra and extensions of quantum mechanics
• Some results on the rotated infinitely deep potential and its coherent states
• Spectral analysis of a selected non self-adjoint Hamiltonian in an infinite dimensional Hilbert space