Abstract
The energy spectrum of the quasiparticles of a one-dimensional chain of half-integral spins with a simple form of interaction, situated in an inhomogeneous magnetic field, is calculated in second-order perturbation theory. It is shown that the mixing of the levels is proportional to the squares of the perturbing inhomogeneities of the field. It is shown that, for a sufficiently large mean value of the magnetic field, the shift of the levels relative to their unperturbed values is symmetric. For small mean values of the magnetic field the higher levels are shown to shift to a greater degree than those situated closer to the ground state.
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