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

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.