We study the behavior of the spectrum of the Dirac operator together with a symmetric W^1,∞-potential on a collapsing sequence of spin manifolds with bounded sectional curvature and diameter losing one dimension in the limit. If there is an induced spin or pin⁻ structure on the limit space N, then there are eigenvalues that converge to the spectrum of a first order differential operator D on N together with a symmetric W^1,∞-potential. In the case of an orientable limit space N, D is the spin Dirac operator D^N on N if the dimension of the limit space is even and if the dimension of the limit space is odd, then D=D^N⊕−D^N.