A method is developed for calculating for a liquid metal the total number of electronic states below an energy E. The method remains valid when the electron-ion pseudopotential is energy dependent. It is based upon an idea of Lloyd (1967), which we have extended and developed into a form suitable for numerical calculation. Calculations for liquid bismuth reveal no sharp structure in the density of states. The bandwidth for five valence electrons per atom is 1.18 Ry, which corresponds to a bandwidth effective mass of 0.63 electron mass, compared with the first order perturbation estimate of 0.87.
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Chan et al. (1971) studied this question.
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