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An effective Hamiltonian to describe the dynamics of the center coordinates of the cyclotron motion is presented. The tail states of the Landau subbands are investigated by means of the effective Hamiltonian for the case of long-range random potentials. Especially the state density in the tail is obtained by the WKB approximation. The mobility edge is roughly estimated by the classical percolation theory and compared with experimental results.
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Masaru Tsukada (1976) studied this question.
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