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Density of states of one-dimensional random potentials

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1 Author(s)
Paul Erdos ; Institute of Theoretical Physics, University of Lausanne, CH-IO15, Switzerland

Following an introduction to the early history of the theories of the density of electronic states in one-dimensional structures, pioneered, among others, by R. Landauer and J. C. Helland, a particular model, that of a multistep random potential, is discussed. It is shown that Kolmogorov-type equations can be obtained for the probability distribution of the phase of the wave function, and, by solving these equations, the density of states may be calculated. An analogy with the classical rotator in a random force field is worked out, and helps in visualizing the results.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

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IBM Journal of Research and Development  (Volume:32 ,  Issue: 1 )