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An elementary derivation of Lloyd's formula valid for full-potential multiple-scattering theory

Rudolf Zeller

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Lloyd's formula is an elegant tool in multiple-scattering theory. It implicitly provides an analytical integration over energy and over all space and directly gives the number of states as a function of energy. The usual derivations of Lloyd's formula are involved and the range of their applicability is not obvious. It is the purpose of this paper to give a derivation which requires only elementary mathematical manipulations. The result is valid for potentials of general shape and for arbitrary complex energies.


PACS

71.15.Ap Basis sets (LCAO, plane-wave, APW, etc.) and related methodology (scattering methods, ASA, linearized methods, etc.)

73.20.At Surface states, band structure, electron density of states

Subjects

Condensed matter: electrical, magnetic and optical

Surfaces, interfaces and thin films

Dates

Issue 36 (15 September 2004)

Received 5 July 2004

Published 27 August 2004



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