Restricted three particle quantum walk on ${\bf Z_{\bf +}}$: explicit solution

R. Iasnogorodski, V.A. Malyshev, A.A. Zamyatin

2018, v.24, №2, 273-296


We consider 3 particles on ${\bf Z}{}_{+}$. 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.

Keywords: quantum walk, discrete Hamiltonian, essential spectrum, point spectrum, discrete spectrum


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