Restricted three particle quantum walk on ${\mathbf{Z}}_{+}$: explicit solution

Abstract

We consider 3 particles on $\mathbf{Z}{}_{+}$. One of them has infinite mass and stands still at $0$. The particles interact only if all of them are at the point $0$. We give a full description of essential, point and discrete spectra of the corresponding hamiltonian.

24 pages