  We consider a mobile impurity particle injected into a one-dimensional
quantum gas. The time evolution of the system strongly depends on whether the
mass of the impurity and the masses of the host particles are equal or not. For
equal masses, the model is Bethe Ansatz solvable, but for unequal masses, the
model is no longer integrable and the Bethe Ansatz technique breaks down. We
construct a controllable numerical method of computing the spectrum of the
model with a finite number of host particles, based on exact diagonalization of
the Hamiltonian in the truncated basis of the Bethe Ansatz states. We
illustrate our approach on a few-body system of 5+1 particles, and trace the
evolution of the spectrum depending on the mass ratio of the impurity and the
host particles.
