Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model

Cannata, F.; Ioffe, M. V.; Nishnianidze, D. N.

Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model

Authors

Cannata, F.

Ioffe, M. V.

Nishnianidze, D. N.

Description

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.
14 pages