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COMBINED DIFFUSION OF PHOTONS AND EXCITED ATOMS

B.A. Beklenko

Published Jan 1, 1960• 0 citations
OpenAlex

Abstract

A Green's function is derived for the equation describing the combined diffusion of photons and excited atoms in an infinite homogeneous space. The asymptotic properties of the equation are analyzed, and the physical conditions under which certain mechanical transposition can be neglected are determined. (tr-auth)

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Progress of Theoretical Physics•Apr 1, 1962•12 citations
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A new method for solving the Schrödinger equation of a particle moving in one dimension in a given static potential is presented in this paper. We start from the observation that the density matrix corresponds to a Laplace transform of Green's function, and satisfies a diffusion-type equation which may be regarded as representing a certain limit of a discrete Markoffian random walk process. Our method of solving the Schrödinger equation is to divide the space occupied by the system into non-overlapping regions, in each of which the Schrödinger equation can be solved. We then introduce a path concept so as to synthesize the solutions for the various regions and thereby formulate the one-particle Green's function. As an application of this formulation, the energy bands of a one-dimensional infinite system are treated. The condition for the existence of impurity band is derived, which qualitatively supports Anderson's theory on the absence of diffusion in certain random lattices.