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arXiv · 0806.4490

Pseudo supersymmetric partners for the generalized Swanson model

A. Sinha·P. Roy
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Abstract

New non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., $ H_- = {\cal{A}}^{\dagger} {\cal{A}} + α{\cal{A}} ^2 + β{\cal{A}}^{\dagger 2} $, where $ αβ$ are real constants, with $ α\neq β$, and ${\cal{A}}^{\dagger}$ and ${\cal{A}}$ are generalized creation and annihilation operators. It is shown that the initial Hamiltonian $H_-$, and its partner $H_+$, are related by pseudo supersymmetry, and they share all the eigen energies except for the ground state. This pseudo supersymmetric extension enlarges the class of non Hermitian Hamiltonians $H_{\pm}$, related to their respective Hermitian counterparts $h_{\pm}$, through the same similarity transformation operator $ρ$ : $ H_{\pm} = ρ^{-1} h_{\pm} ρ$. The formalism is applied to the entire class of shape-invariant models.

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A. Sinha, P. Roy. 2008-06-27. Pseudo supersymmetric partners for the generalized Swanson model. https://doi.org/10.1088/1751-8113/41/33/335306

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