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arXiv · 2109.14540

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

Francisco M. Fernández
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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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Francisco M. Fernández. 2021-09-28. On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation. https://doi.org/10.1016/j.aop.2022.169008

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