On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation

Abstract

We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to Hermitian operators. In the class of Hamiltonian operators discussed here the transformation is given by a Hermitian, positive-definite, diagonal operator. We show that there is an important difference between open boundary conditions and periodic ones. We illustrate the theoretical results by means of two simple, widely used, models.

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Cited by in corpus (5)

• Complex tridiagonal quantum Hamiltonians and matrix continued fractions
• Quantum singularities in a solvable toy model
• Few-grid-point simulations of Big Bang singularity in quantum cosmology
• Resonances and continued-fraction Green's functions in non-Hermitian Bose-Hubbard-like quantum models
• Extremely broken generalized $\mathcal{P}\mathcal{T}$ symmetry