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The exact solution of the Schr\"odinger equation for the one-dimensionalsystem of interacting particles with the linear dispersion law in an arbitraryexternal field is found. The solution is reduced to two groups of particlesmoving with constant velocities in the opposite directions with a fixeddistance between the particles in each group. The problem is applied to theedge states of the 2D topological insulator.

Exact solution for many-body Hamiltonian of interacting particles with linear spectrum