# Tridiagonality, supersymmetry and non self-adjoint Hamiltonians

## TL;DR

This paper explores non self-adjoint tridiagonal Hamiltonians and their supersymmetric versions, focusing on eigenstate analysis, recursion formulas, and biorthogonal vectors, with applications to bi-squeezed states.

## Contribution

It introduces new recursion relations and biorthogonal families for non self-adjoint Hamiltonians and their supersymmetric counterparts.

## Key findings

- Eigenstates lead to interesting recursion formulas.
- Biorthogonal families of vectors are constructed.
- Connections with bi-squeezed states are established.

## Abstract

In this paper we consider some aspects of tridiagonal, non self-adjoint, Hamiltonians and of their supersymmetric counterparts. In particular, the problem of factorization is discussed, and it is shown how the analysis of the eigenstates of these Hamiltonians produce interesting recursion formulas giving rise to biorthogonal families of vectors. Some examples are proposed, and a connection with bi-squeezed states is analyzed.