It is shown that a linear chain consisting of a large number of atoms of spin {} with nearest neighbor ferromagnetic or antiferromagnetic interactions is mathematically equivalent to a one-dimensional Fermi gas with two-body forces. This equivalence is used to construct a wave function for which the expectation value of the energy lies between the two approximations obtained by Hulth\'en. Also, a perturbation treatment is given which permits, in principle, to obtain the exact antiferromagnetic ground state.
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Sergio Rodríguez (1959) studied this question.
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