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The completeness, together with the orthonormality, of the eigenfunctions ofthe Dirac Hamiltonian with a step potential is shown explicitly. Theseeigenfunctions describe the scattering process of a relativistic fermion offthe step potential and the resolution of the identity in terms of them(completeness) is shown by explicitly summing them up, where appropriatetreatments of the momentum integrations are crucial. The result would bringabout a basis on which a field theoretical treatment for such a system can bedeveloped.

Completeness of scattering states of the Dirac Hamiltonian with a step potential