ANALYTIC PROPERTIES OF ONE-DIMENSIONAL BLOCKFUNCTIONS,
Abstract
The analytic properties as functions of wave number k of the solutions of a single-electron Schrodinger equation for one-dimensional periodic potentials with inversion symmetry have been treated by Kohn for nonconnected energy bands. Kohns results are generalized in order to include the case of missing inversion symmetry and connected bands; already known results are reviewed to a certain extent in order to treat the generalizations in a closed frame. A simple proof is given, that the Schrodinger equation, considered as differential equation with initial conditions, has solutions which are holomorphic as functions of the parameter E throughout the whole complex E-plane even in the very singular cases when the potential contains 8-functions or infinities which are not too strong. The Floquet functions are then constructed in the usual way. The asymptotic behavior of the functions for large (E) is discussed in a detailed way and some remarks are made in the case of singular potentials. The inverse of the function E(k) is also considered. The structure of the Riemannian surface of E(k) is obtained. The Bloch functions are normalized without assuming inversion symmetry for the potential. Their analytic structure turns out to be somewhat more complicated than that of E(k). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 15, 1963
- Accession Number
- AD0432039
Entities
People
- Gert Eilenberger
Organizations
- Uppsala University