Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

TL;DR

The paper extends a method for generating non-isospectral Hamiltonians with related eigenvectors, including cases involving crypto-hermitian Hamiltonians, broadening the scope of intertwining operator techniques.

Contribution

It introduces a novel procedure to construct Hamiltonians with different spectra while maintaining eigenvector relations, applicable to crypto-hermitian systems.

Findings

New method for non-isospectral Hamiltonian construction

Extension to crypto-hermitian Hamiltonians

Broader applicability of intertwining operator techniques

Abstract

We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,xx^\dagger]=0$ and $x^\dagger x$ is invertible, a second hamiltonian $h_2$ with the same eigenvalues as $h_1$ and whose eigenvectors are related to those of $h_1$ by $x^\dagger$. Here we extend this procedure to build up a second hamiltonian, whose eigenvalues are different from those of $h_1$, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian hamiltonians.