Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials

A set of r non-Hermitian oscillator Hamiltonians in r dimensions is shown to be simultaneously diagonalizable. Their spectra are real and the common eigenstates are expressed in terms of multiple Charlier polynomials. An algebraic interpretation of these polynomials is thus achieved and the model is used to derive some of their properties.

► A set of r non-Hermitian oscillator Hamiltonians in r dimensions is presented.
► Their spectra are real.
► The common eigenstates are expressed in terms of multiple Charlier polynomials (MCP).
► This “integrable” model allows to interpret structural formulas of the MCPs.