Titlebook: Localized Excitations in Solids; R. F. Wallis Book 1968 Springer Science+Business Media New York 1968 applied physics.physics.solid

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A Method for Determining Strict Bounds on the Frequencies of Localized Phononsts of finding strict and close upper and lower bounds for the local-mode frequencies by means of a simple matrix calculation; it is not a Green’s function method, and therefore does not depend upon the availability of tabulated data. A full account of the method, with proofs and references to basic

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