Eigenstates of an electron in ordered and disordered ensembles of scatterers

Localization of Electronic States in Disordered Tight‐Binding Systems. I. Derivation and Study of the Model

“…Using MST a general solution to (1) can be given [15] under the supposition that the solution in each single-site potential V , is known. Generally, in order to obtain tractable equations one has to make restrictions either to the potential (muffin-tin approximation which is suitable for the dense-packed structures of metals) or to the single-site Hilbert space 33.)…”

“…The energy eigenvalues Et of a particle in the system of N' potentials V , can be found from the diagonaliza,tion of the matrix where AT$ is a normalization factor. Remember that in [15] instead of the matrix (4) another, generally non-Hermitian representation was obtained. From a physical point of view it is not quite understandable why in the original non-Hermitian representation the potential V , is distinguished from Vp.…”

“…from the multicentre Hamiltonian of a single electron in a disordered system. The basis ingredients of the theory are the multiple-scattering theory (MST) [15] and the recursion method (RM) [8, 01, where the MST leads to the desired representation of the Hamiltonian and the RM is a means to solve the obtained equations. Hitherto the RM was above all used as a useful numerical mcthod, whereas here we are interested in analytical results.…”

“…We prefer directIy to start from MST in zeroth order of perturbation theory within which the matrix of overlaps on principle does not appear [15]. In this way a non-Hermitian Hamiltonian matrix is obtained which is approximately replaced by a Hermitian one.…”