The integrated density of states N(E) for a particle in a set of arbitrarily located repulsive δ-function potentials is studied. Upper and lower bounds for N(E) are given. For the completely disordered chain we derive the asymptotic form N(E)~ae^-b√E, E→0⁺. For a chain with short-range order a simple proof of the existence of forbidden gaps based on the present method is briefly sketched.
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T. P. Eggarter (1972) studied this question.
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