Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model

Details Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model

2007-04-17

arxiv.org/abs/0704.2219v1

Phys.Lett.A369:9-15,2007

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1016/j.physleta.2007.04.056

We study a two-dimensional exactly solvable non-Hermitian $PT-$non-symmetric quantum model with real spectrum, which is not amenable to separation of variables, by supersymmetrical methods. Here we focus attention on the property of pseudo-Hermiticity, biorthogonal expansion and pseudo-metric operator. To our knowledge this is the first time that pseudo-Hermiticity is realized explicitly for a nontrivial two-dimensional case. It is shown that the Hamiltonian of the model is not diagonalizable.

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