Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

Abstract

We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,x{x}^{†}]=0$ and $x^{†}x$ 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 $x^{†}$. 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.

in press in Phys. Lett. A

References in corpus (3)

• Three-Hilbert-Space Formulation of Quantum Mechanics
• Vector coherent states and intertwining operators
• Non linear pseudo-bosons versus hidden Hermiticity

Cited by in corpus (2)

• $PT$-symmetric graphene under a magnetic field
• Non self-adjoint Hamiltonians with complex eigenvalues