Excited electrons and holes a r e subject to inelastic collisions with other electrons and this leads to finite lifetimes of these states even in perfect crystals.Lifetimes of individual electrons and holes have recently been connected with peak widths in angle resolved photoemission from crystals /1, 2/, SO that these important characteristics become experimentally achievable. In the one-electron picture the lifetimes can be theoretically described by means of optical potentials /3/. We shall treat a one-dimensional model of a crystal in the nearly free electron approximation. The electron Hamiltonian H = T + V is then (in atomicwhere g is a reciprocal lattice vector, related to the potential periodicity a by g = 2x/'a. In contrast to the usual band structure calculations with real Vo and 1) Na Slovance 2, 18040 Praha 8 -LibeK, CSSR.