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The Kronig-Penney model, an exactly solvable one-dimensional model of crystalin solid physics, shows how the allowed and forbidden bands are formed insolids. In this paper, we study this model in the presence of both strongspin-orbit coupling and the Zeeman field. We analytically obtain fourtranscendental equations that represent an implicit relation between the energyand the Bloch wavevector. Solving these four transcendental equations, weobtain the spin-orbital bands exactly. In addition to the usual band gap openedat the boundary of the Brillouin zone, a much larger spin-orbital band gap isalso opened at some special sites inside the Brillouin zone. The $x$-componentof the spin-polarization vector is an even function of the Bloch wavevector,while the $z$-component of the spin-polarization vector is an odd function ofthe Bloch wavevector. At the band edges, the optical transition rates betweenadjacent bands are nonzero.

Energy spectrum, the spin polarization, and the optical selection rules of the Kronig-Penney superlattice model with spin-orbit coupling