Bound states and resonances of the energy operator of a single-magnon spin-polaron system

A spin–polaron bound state for arbitrary dimensions, and also a spin–polaron resonance – a quasistationary state – are investigated. In the case of dimensions $\nu=1$ and 2, it is shown that for all values of the total quasimomentum $\lambda$ and for arbitrary parameters of the system there exists a unique “spin–polaron” bound state. In addition, uniqueness of the physical resonance for $\nu=1$ and $A\not=0$ is proved, and for small $A\not=0$ and any dimension $\nu$ the width of the physical resonance is also found.