Rudolf Zeller 2004 J. Phys.: Condens. Matter 16 6453 doi:10.1088/0953-8984/16/36/011
Rudolf Zeller
Show affiliationsLloyd'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.
73.20.At Surface states, band structure, electron density of states
Issue 36 (15 September 2004)
Received 5 July 2004
Published 27 August 2004
Rudolf Zeller 2004 J. Phys.: Condens. Matter 16 6453
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Takahiro Nishimura et al 2009 J. Micromech. Microeng. 19 125002
Stewart J Clark and Philip P Rushton 2004 J. Phys.: Condens. Matter 16 4833
Sang Bub Lee and Hisao Nakanishi 2000 J. Phys. A: Math. Gen. 33 2943
Erich J Mueller et al 2001 J. Phys. B: At. Mol. Opt. Phys. 34 4561
F. S. Masset et al. 2006 ApJ 652 730
Gleb Arutyunov et al 2007 J. Phys. A: Math. Theor. 40 3583
S E Derkachov et al 1990 J. Phys. A: Math. Gen. 23 5563